The midfielder said he will take fond memories from his two seasons at the Lane and credits Martin for improving him as a player, while thanking the fans for the backing they have given him since he made his debut.
"Martin is a great manager and has done an enormous amount for my career," said Michael. "Without any doubt he has helped develop me into a better player. He gave me a chance when I needed it, stood by me and I will always thank him for that."
"I'd like to thank the fans as they've been fantastic to me as well. This is a football decision, a decision not driven by money. It's an offer that has come at the right time for me both professionally and personally and I felt I couldn't turn it down.
"I've had a great time at Spurs and the Club has been brilliant for me. There is an excellent squad full of top players and a number of younger lads coming through the ranks as well. I can only see successful times for the Club in the future."
Manager Martin Jol added: "Michael played nearly all the games for us after coming on in the second half against Charlton the season before last and never looked back. He always gave his best and was a wonderful servant. I'm sure he will do well at Manchester United because he is very talented and we will miss having him around the Lodge."
Michael Carrick on Monday evening completed his transfer to Manchester United with the agreement of personal terms and passing of a medical.