Rooney, 31, played 559 times for United, scoring 253 goals.
He won five Premier League titles and each of the Champions League, Europa League and FA Cup once after joining from Everton for £27m in 2004.
Rooney, who has signed a two-year deal, said he was "ecstatic" and his "first game back will be an emotional day".
"It's a great feeling to be back. I cannot wait to meet the lads, get on the training pitch and then get on the pitch to play," he added.
Rooney's return comes as United look set to sign Everton striker Romelu Lukaku, with a £75m deal for the Belgium international agreed between the two clubs.
Everton confirmed Rooney will wear the number 10 shirt previously worn by Lukaku.
"I'm not just coming back because it's the team I support, the team I grew up playing for - I'm coming back because I feel the club can move forward and be successful," said Rooney, who scored 17 goals in 77 games in his first spell at Goodison.
"I want to be part of it. There will be pressure on me to perform, but I'm ready to go. I believe I can help move this club forward and be more successful on the pitch."
Rooney says when he spoke to Everton manager Ronald Koeman, he "saw it in his eyes that he wanted me to be part of his team".
He added: "It was a no-brainer for me and the only place I was going to go."
Rooney said he told his agent Paul Stretford to "go and speak to them, let's make it happen" when he found out Everton were interested in signing him and it "was obvious I was going to be leaving Manchester United this summer".
"There were other options there but once I knew that Everton wanted me to come back then it was the only option for me," he added.
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Koeman began talking about Rooney's potential return as far back as October, stating he would be "pleased" to sign England's all-time leading goalscorer.
On Sunday, he said: "Wayne has shown me that ambition that we need and that winning mentality - he knows how to win titles and I'm really happy he's decided to come home.
"He loves Everton and he was desperate to come back. He is still only 31 and I don't have any doubts about his qualities. It's fantastic he's here.
"We have a lot of young players and sometimes in life you need somebody who you look up to, who you learn from. That was also one of the messages when we spoke about on and off the pitch what his function will be in the team.
"One of the functions for Wayne is to show the rest of the team why he is - and still is - that player."
Rooney, who was often left out of United's starting line-up by manager Jose Mourinho last season, appeared in 25 league games - the fewest he has played in one season. His total of eight goals in all competitions was also the lowest of his career.
He also lost his place in the England squad, but has not retired from international duty and needs six more caps to equal goalkeeper Peter Shilton's all-time record of 125 appearances.
Rooney was an unused substitute as United beat Southampton to win the EFL Cup in February, and made only a brief appearance at the end of the Europa League final victory over Ajax in May.
In his 13 seasons with United, he finished as top scorer five times and shared the honour with Cristiano Ronaldo in another campaign. He was also named fans' player of the year twice.
"It is no secret that I have long been an admirer of Wayne," said Mourinho. "He has been a model professional throughout his time at the club and will remain in the history books for many years to come.
"It is never easy to see a great player playing less football than he would like and I could not stand in his way when he asked to go back to Everton.
"His experience, focus and determination will be missed and I wish him well for the future."
Executive vice-chairman Ed Woodward added: "Who can forget his storybook debut hat-trick against Fenerbahce, the spectacular overhead kick against Manchester City and the countless match-winning performances in his time here?
"But after much discussion, the club has decided to accept his request to rejoin his boyhood team."
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Andy Mitten, editor of fanzine United We Stand: "The move is best for all parties.
"Rooney will be remembered well by United fans when the dust settles, a club legend who scored more goals than anyone and was a leading light in one of United's greatest sides.
"Reaching three European Cup finals in four years shows how good that team was. At his best, between 2004 and 2011, he was the finest British player of his generation.
"Rooney's performances dropped, and being linked with Chelsea and Manchester City did his popularity no favours either, but he's scored some of the greatest goals I've ever seen.
"As a journalist who has interviewed him several times over 12 years, I watched him mature, become more interesting and grow into being a respected Manchester United captain."
Rooney was brought up by parents Jeanette and Wayne in the Croxteth area of Liverpool alongside brothers Graham and John, with all five members of the household avid Everton supporters.
He joined the Toffees at the age of nine and quickly built a reputation as a precocious talent, scoring 114 goals in 29 matches for the under-10 and under-11 sides.
David Moyes gave him his first-team debut in August 2002, and he quickly became a regular starter, scoring his first Premier League goal - a last-minute winner against Arsenal - five days before his 17th birthday.
I've kept it quiet for the last 13 years, but I've actually been wearing Everton pyjamas at home with my kids.
The goal led to Arsenal manager Arsene Wenger describing Rooney as "the biggest English talent I have seen since I arrived in this country". Wenger added: "He has everything you dream of for a front player - intelligent feet, quick reactions."
Rooney became one of world football's highest-paid teenagers with his boyhood club, but handed in a transfer request in August 2004, leading to him being signed by Sir Alex Ferguson for what was the highest fee paid for a player under 20.
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BBC Sport's Simon Stone: Rooney has been slowly eased out of the first team, without there being one single pressure point that signalled a change in Mourinho's thinking.
The Portuguese has consistently backed Rooney in public - saying as recently as May that he would be "very happy" if the striker stayed at Old Trafford.
But Rooney did not take the chances he was afforded by Mourinho last season, and that made his departure inevitable once Everton pursued their interest.
Rooney signed a new four-and-a-half-year contract during the 2013-14 campaign, which included the option of a further season, but the Old Trafford club had no intention of triggering that clause.
United have waived a fee and may also be funding part of Rooney's £13m wages.
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Bill Kenwright was crying. 'They're stealing our boy, they're stealing our boy,' he told his mother.
"He's one of those players that, whenever he gets the ball, something seems to happen." Then England manager Sven-Goran Eriksson, 2003.
"Wayne is only 20 and without question the best young player I've ever seen." Then Manchester United manager Sir Alex Ferguson, 2005.
"Wayne Rooney is the golden boy of English football. Don't kill him because you will need him." Eriksson again, 2006.
"We've done nothing but help him since he's been at this club. We cannot quite understand why he would want to leave." Ferguson again, 2010.
"I think crazy things happen around him also. He is an impulsive guy like me. In football no-one is perfect. You learn from your mistakes and I like that with him. He is himself; I think that is very important. That is one English player I like more than anyone." Zlatan Ibrahimovic, 2013.
"I felt he was struggling to get by people and had lost some of his old thrust. As time wore on, I felt he struggled more and more to do it for 90 minutes." Ferguson in his autobiography, 2013.
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"He's been through that generation with the likes of Steven Gerrard and Frank Lampard. He really feels like he's the dad figure if you like. He puts his arm around us, brings us together, gets us going." Arsenal midfielder Jack Wilshere, October 2014.
"I miss playing with Rooney. Maybe we will play together again one day. He was so powerful, I was calling him 'Pitbull'. The power of Wayne Rooney is his mentality and strength and he never stops." Cristiano Ronaldo, 2015.
"For me he is the great English player of the generation. What he is capable of doing on the field is very special, and he is one of the few players that would improve any squad in Europe." Barcelona and Argentina forward Lionel Messi, 2016.
"Cristiano had an absolute desire to be the best individual in the world. Wayne would say: 'I want to be the world's best but I'll do it by being a team player.' That has not allowed him to be the 40-goals-a-season man he could have been." Former Manchester United and England defender Rio Ferdinand, 2017.
United winger Jesse Lingard: "All the best skipper in the next chapter of your amazing career. Been an absolute pleasure and learned so much."
United midfielder Ander Herrera: "One day I will be able to tell my grandkids I played with you. All the best and thank you."
Former United defender Gary Neville: "All the best Wayne Rooney and congratulations on a great United career. The best striker I played with and saw at the club."
Rooney's wife, Coleen: "The time has come to leave Man Utd .... 13 great years at the club! Thank you all for making our family so welcome and treating us so well."
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Manchester United record goalscorer Wayne Rooney has rejoined Everton for an undisclosed fee, 13 years after leaving the Merseyside club.