The 20-year-old England international passed a medical and agreed personal terms with the club on Thursday in a deal reported to be worth £20m.
Henderson, the club's first summer signing, signed what Liverpool described as 'a long-term deal'.
"I'm over the moon, overjoyed to be here and I'm really looking forward to it," Henderson told the Liverpool website.
"Obviously it's hard to leave your local club. I'm a Sunderland lad, I've supported them all my life.
"But I'm really looking forward to the future now and obviously this is a massive opportunity for me. I'm really excited by it."
Steven Gerrard is one of the best players in the world, you want to be playing with him and training with him to try and improve yourself as a player
The midfielder, whose one and only cap for England came last November against France, has now joined the England Under-21 squad in Denmark ahead of the European Championship.
The Black Cats had rejected Liverpool's previous offer for the player, which was thought to be worth £16m.
Striker David Ngog, 22, could move in the opposite direction as part of the deal, but that is yet to be confirmed.
Henderson will provide competition in the Reds' midfield, which already boasts internationals Steven Gerrard, Lucas Leiva, Raul Meireles and Christian Poulsen.
"Coming to a massive club like Liverpool, there is always going to be competition," added Henderson. "Hopefully I can keep working hard, keep improving, and get my chance on the pitch.
"(Gerrard) is one of the best players in the world, you want to be playing with him and training with him to try and improve yourself as a player. Hopefully I can learn a lot from him."
Reds director of football Damien Comolli said of the deal: "I'm very pleased because he was one of the targets we had and when you get your first target it's always a good sign because you think the others will come through as well.
"He has got all the skills technically that we needed," he added. "He's good with the ball, he's creative, he's got good passing, he's physically very good.
"That's everything we wanted in a midfielder and he's versatile as well. For manager Kenny Dalglish he will be the player we wanted."
The Sunderland-born Henderson, who had a loan spell at Coventry City early in his career, signed a five-year contract at the Stadium of Light in April 2010.
He came to prominence as Steve Bruce's Black Cats made a fine start to the season and was rewarded with an England call-up by coach Fabio Capello.
And though his form dipped as Sunderland struggled in the second half of the campaign, Henderson is still regarded as one of England's brightest young prospects.
Manchester United had been regarded as the long-time favourites to sign Henderson after he made an outstanding start to last season, but their interest cooled and manager Sir Alex Ferguson has moved on to other midfield targets.
Liverpool have completed the signing of Jordan Henderson from Sunderland.