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.
He said: “Joining Manchester United is a dream come true for me.
“The club is such an institution in Denmark, it’s an honour to come here.
“I’m looking forward to playing and training alongside some of the great players in football today.
“I can’t wait to be part of this team and to make my contribution to keeping the team at the top of the game.”
