The England under 21 star has impressed since breaking into the first team and was played up front with Michael Owen in the 3-1 win over Wolfsburg in the Champions League.
Sir told the club’s official website: "We are delighted. We see Danny as one of the great young players who has emerged from the academy.
"He will have a terrific career and we are glad that he has placed his trust in us with his future."
Welbeck was over the moon with the deal, he 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."