Manager Sir Alex Ferguson said: "We are delighted. We see Danny as one of the great young players who has emerged from the academy.
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Welbeck added: "I am really happy, there was never a doubt that this is where I want to be.
"I am enjoying every minute and learning so much from all the great players that are here. I would like to thank Sir Alex, the club and the fans for all their support."
Ferguson, meanwhile, has dismissed rumours linking Ben Foster with a loan move away from Old Trafford in January.
Foster has struggled for first-team action with United this season and has fallen behind Tomasz Kuszczak in the pecking order.
"Nothing is going to happen with Ben. He is here and this is where he stays," Ferguson said.