Southgate succeeds Stuart Pearce, whose contract was not renewed by the Football Association following a disappointing European Championships campaign in June.
In Pearce's absence senior boss Hodgson took charge of the Young Lions for a 6-1 win over Scotland earlier this month and he is hopeful that Southgate can also get the best out of the squad.
"I know Gareth well and he has the right philosophy and approach to football, and I'm very much looking forward to working with him," he said.
"Having taken the Under-21s earlier this month I'm aware of the talent that exists within the group, so it is a great opportunity looking ahead to the tournament in two years' time."
Southgate's first task will be preparing a squad for the 2015 European Under-21 Championship in the Czech Republic, with the first qualifier against Moldova taking place in Reading on September 5 before a trip to Finland four days later.
The 42-year-old will report to the FA's director of elite development, Dan Ashworth.
"I look forward to working with Gareth," said Ashworth. "He came through a comprehensive and thorough interview process, showing a real understanding of our need to ensure a consistency in the style of play across the England development teams at every level.
"Gareth shares our belief that now is an important moment for English football, it is the time for change and his ideas and experience will be crucial to the direction we wish to take the development teams in future."
Southgate was himself the FA's head of elite development between February 2011 and July 2012 and had been earmarked as its technical director before deciding against taking up the post.
Southgate will also oversee the coaches with responsibility for the Under-20s through to the Under-16s, support the FA's contribution to EPPP (Elite Player Performance Plan) through regular club visits, and help develop the FA's tournament strategy.
"I'm delighted to get this role and extremely excited about the prospect of working with the best and brightest young players in the country," he said.
"I'm a proud Englishman and playing for my country was the pinnacle of my playing career.
"Since retiring as a player I have gained a lot of knowledge and experience of the game both here and abroad, and I'm eager to play my part in preparing players to compete at the highest level.
"Whenever any team steps onto the pitch for England, being successful is of huge importance, but it is also about developing a clear style of play that can allow our talented young players to flourish."