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."

Sebastian Prodl is suspended while Christian Kabasele, Craig Cathcart and Younes Kaboul are all out injured.
Manchester City captain Vincent Kompany should be fit despite being substituted during the 3-1 win over West Brom.
John Stones has also recovered from a groin strain and could replace Nicolas Otamendi in defence.
Steve Wilson: "Pep Guardiola's been saying some interesting things this week. Firstly that his side's performance this season would have got him sacked at the kind of club he's been accustomed to working at.
"Then he asked an interviewer to give him one good reason to think that the English league is anything special compared to Spain, Italy and Germany.
"I'm certainly not saying that Guardiola is wrong - just that it's odd that he was willing to say this stuff. You might interpret it as a pointed signal to those he works with at City to up their game if they want to get to his level.
"Speaking of managers, Walter Mazzarri has been told to pack his bags with Watford issuing a statement remarkable only for its brevity.
"The Hornets are on their longest losing streak in nine years - should they lose again on Sunday it will be their longest for 44 years. Enough said."
Twitter: @Wilsonfooty
Watford head coach Walter Mazzarri: "I would like to thank the main characters of this season - the players and the fans.
"Our fans have always been extraordinary with their participation and with their fantastic passion for the whole season.
"Also I thank the players, who have always given 200 per cent of what they had, always going further and pushing their limits."
Manchester City manager Pep Guardiola: "It's a crucial game for us absolutely - a final. It's in our hands. We have to go there and win. We have won three in a row but we still have 95, 96 minutes to fight.
"Watford have had a good season. They are safe. We have to be careful.
"We are going to make changes [in the summer]."
I had been wondering for a while what was going to happen to Watford boss Walter Mazzarri, and it was no surprise when it was announced this week that he will be leaving.
I think the Hornets will play well in his farewell game but I still think Manchester City will get the win they need to secure third place.
Prediction: 0-3
Lawro's prediction v rock band Royal Blood.
Head-to-head
Watford
Manchester City
SAM (Sports Analytics Machine) is a super-computer created by @ProfIanMcHale at the University of Salford that is used to predict the outcome of football matches.
Former Watford and Coventry boss Aidy Boothroyd has been confirmed as manager of the England Under-21 team.
[NEXT_CONCEPT]
Watford could be without up to six central defenders, with Adrian Mariappa (knee) and Miguel Britos (calf) facing late fitness tests.