The Blades, relegated to the third tier for the first time since 1988 with one game to go this season, won just four of their 24 games under Adams, 49, who is now expected to apply for his old job at managerless Port Vale.
Adams, relieved of his duties by Blades chairman Kevin McCabe on Tuesday, said: "Obviously I'm very, very disappointed with the decision, but I still wish Sheffield United all the best.
"I'm a Blade and will always be a Blade, so I'm just sorry that my move here has not worked out. I pass on my thanks to the fans and would still like to think that they regard me as one of them.
"To carry the support of so many of them in some pretty dark days was very much appreciated.
"But most of all I wish the McCabes well because if anyone deserves success it is Kevin and his family."
Source: PA
Source: PA