And the 41-year-old has now been officially confirmed as the successor to John Toshack, signing a three-and-a-half year contract.
Speed told the club’s official website: “This has been an extremely difficult decision for me on many levels and one that I had to give great consideration to because of my genuine attachment to Sheffield United, especially as I was only made manager less than four months ago.
“I will always be grateful for being given that opportunity, not least because it has helped lead to where I am now.
“In a way the Welsh job has come too soon for me because I feel that I have unfinished business here, and I owe many people, including players, officials and staff an awful lot.
“But my main concern and thanks are reserved for the supporters who have been so patient and supportive. They really deserve a successful football team and I would have been more than happy to stay and try and play my part in that.
“But, being passionate supporters themselves, I hope they can understand why the lure of managing my country was so strong and why, in the end, I felt that I had to accept the challenge.
“Sheffield United is a smashing club which I have been proud to work for and I will never forget how it has dealt with me in a professional but honourable manner.
“This has been the most difficult decision of my life and although I have felt compelled to follow my heart, I wish the supporters and everyone connected with the Club every success.
“I know how resilient the Blades faithful are and urge them to get behind the team on Saturday against Swansea.”
Blades CEO Trevor Birch added: “We are obviously disappointed and this would not have been entertained had it been another club side but having received the approach we felt obliged to give Gary the option of discussing the position with the Welsh FA.
“We didn't want to lose him but we have to respect Gary's decision given the uniqueness of the opportunity. This is a prestigious appointment and we wish him every success and thank him for his contribution to the club over the last three years.”
First team coach John Carver has been installed as caretaker manager.