"Celtic are delighted to announce that Roy Keane has signed for the club," read a statement carried by the club's official website.
"The self-confessed Celtic fan has fulfilled a long-held dream by joining the Hoops and his contract will see him remain at Celtic Park initially until June 2007."
The Irishman has surprisingly ended his contract at Old Trafford in November after repeated bust-ups with Manchester United boss Alex Ferguson.
Keane has been linked with several Premiership clubs in addition to Real Madrid but opted to join Celtic whom he said in 1999 he wishes to end his carerr with.
"It's a great move for me. I feel that this is where I belong and I'm here to work hard and win games," Keane told reporters when he was officially introduced at Celtic park.
The 34-year-old midfielder added that he preferred a move to Scotland for a new challenge after 13 seasons with United.
"I've been in the Premiership for a long time and feel I have proved myself there and needed a different environment, different teams, and different grounds," Keane said.
Celtic coach Gordon Strachan praised the move and said that Keane will boost his side's performance.
"He has proved over the last 15 years that he is a competitor. You can't get enough competitors in your squad and this was too good a chance to miss."