The Denmark international, who joined the club from Aalesund in January 2011, has committed himself to United for until the end of the 2015-15 season.
"I'm very pleased to have signed a new contract," Lindegaard told the club's official website. "I'm glad and proud that the manager has shown the confidence he has in me by giving me a new deal.
"There is nowhere in the world I would rather be than right here. The competition for places is tough, as it should be in a club like this. It only makes us better as individuals and, more importantly, stronger as a team.
"It's what I have dreamt of all my life and nothing makes me more proud than wearing the Manchester United badge.”
Though the 28-year-old has largely played as back-up to David De Gea over the past 12 months, he did briefly displace the Spaniard last season before succumbing to injury himself.
Sir Alex Ferguson said: "Anders is still relatively young for a goalkeeper but he has come on leaps and bounds since joining us last year.
"There is healthy competition in the goalkeeping department, which is always good for the team, albeit a headache for me.
"I am delighted he has signed a new contract and also delighted to see that he has clearly returned from the summer break in good shape after the disappointment of suffering an injury last season.”