The 41-year-old was given permission by Sheffield United to speak to the Football Association of Wales after they identified him as their preferred candidate.
"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," Speed said after being presented to the media at a press conference at the Vale of Glamorgan hotel.
On his departure from Bramall Lane, he said: "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."
Source: PA
Source: PA