The Under-20 boss replaces Gareth Southgate, who vacated the role to become England manager after the departure of Sam Allardyce.
Boothroyd, 45, took charge for the U21 side's final two Euro 2017 qualifiers and secured qualification for this summer's finals in Poland.
"I've been at the FA three years; this is the logical next step," he said.
"I believe I am here on merit because I've worked in all four divisions and I've got an understanding of speaking to a League Two manager or a Premier League manager and the problems they have."
Boothroyd was in charge of Watford for three seasons from 2005, initially saving the club from relegation to the third tier before leading them to the top flight in 2006.
The Vicarage Road side finished bottom of the Premier League the following season, then failed to make an immediate return, losing in the play-off semi-finals.
Boothroyd left the following season and had a nine-month spell at Colchester and an 11-month stint at Coventry before taking charge at Northampton in 2011.
The side were bottom of League Two at the time and Boothroyd guided them to safety, and the play-offs the next season, before being sacked in 2013 with the club once again last in the fourth tier.
"You can get stuck in a job and I was very much on a hamster's wheel in my previous jobs," he told BBC Radio 5 live.
"But this has reinvigorated me. I've watched games I could only have dreamed of, met people, been to World Cups and I feel like I've grown massively in the last three years."
Former Watford and Coventry boss Aidy Boothroyd has been confirmed as manager of the England Under-21 team.