The 26-year-old joins United for an undisclosed fee and has signed a contract that will keep him at Old Trafford until the summer of 2014.
Lindegaard will start to train with United straight away, but will not be eligible to play intil January.
United boss Sir Alex Ferguson said: “Anders is one of the brightest young keepers in the game.
“The challenge at Manchester United is always to look to the future and in Anders, we have signed a goalkeeper of great presence and even more promise.
“Having the time to train with him before he is registered will be an important period for him – almost like a pre season to get him integrated with the other players.”
