The 23-year old joined Rovers in January 2008 from Blackburn after impressing during a loan spell at Prenton Park.
Blades boss Kevin Blackwell told the club's official website: "Andy is still young enough to develop and we have been watching him for quite a while.
"We regarded him as one of the best left-backs outside the Premiership and that is reflected by the fact that we beat several other Championship clubs to his signature."
Taylor made 81 appearances for Tranmere and scored three goals.
He added: "When I left Rovers, I could have gone to Preston or Blackpool but chose Tranmere in order to get games and, hopefully, progress well enough to go back up the divisions.
"This is a massive club, a great opportunity, and to be honest as soon as I heard of United's interest and the chance to come here and speak I had no hesitation - it was an easy decision to sign.
"I really enjoyed my time at Tranmere but this move was a great opportunity for me."
Having sold Taylor, new Rovers boss John Barnes is already seeking to make new additions to his squad.
Barnes said: "It was a good offer from Sheffield United and we decided to allow Andy the chance to move to a higher level.
"We're still looking to add to our squad ahead of the season and are talking to a number of clubs about both loan and permanent deals."
Coca Cola Ch'ship Promotion 09/10 Win Outright: Sheff Utd 7/2