The 41-year-old has signed a three-and-a-half-year deal to succeed John Toshack.
Speed: "It's something that's very difficult to turn down when your country comes calling. I'm a very proud man at this moment to be asked to be the manager of Wales.
"These things happen in football, where the timing's not always great.
"I was disappointed to leave Sheffield United because I feel I had a job to do there and was fully committed but obviously when your country comes calling it's a tough decision you have to make. I feel in my heart it's the right one.
"To be fair to them they've been fantastic throughout and made the decision really easy for me.
"I'd like to thank Sheffield United for the opportunity I've been given there both as a coach under Kevin Blackwell and then as a manager."