The former Red Devils midfielder, captain and coach has improved results and morale since being brought in after Ruben Amorim's acrimonious January exit.
Carrick secured Champions League football with three matches to spare and United wrapped up third spot in the Premier League standings with Sunday's 3-2 win over Nottingham Forest - his 11th victory in 16 games.
The 44-year-old was rewarded with a two-year extension, almost a week after a broad agreement was reached.
"From the moment that I arrived here 20 years ago, I felt the magic of Manchester United," Carrick said on Friday.
"Carrying the responsibility of leading our special football club fills me with immense pride.
"Throughout the past five months, this group of players have shown they can reach the standards of resilience, togetherness and determination that we demand here.
"Now it's time to move forward together again, with ambition and a clear sense of purpose.
"Manchester United and our incredible supporters deserve to be challenging for the biggest honours again."
Carrick steadied the ship after Amorim's rocky reign, with the low of August's Carabao Cup exit at Grimsby firmly put in the rear-view mirror as he began his short-term stint by beating Manchester City and Arsenal.
United turned to Carrick because they wanted somebody who understood the club's unique pressures to aid the adaptation process as director of football Jason Wilcox weighed up their options.
Carrick was the unanimous choice in January for a job he competed for with Ruud van Nistelrooy and Ole Gunnar Solskjaer, whose coaching staff he was a part of and now follows in going from stop-gap coach to permanent boss.
"Michael has thoroughly earned the opportunity to continue leading our men's team,'' Wilcox said.
"In the time he has been doing the role, we have seen positive results on the pitch, but more than that, an approach which aligns with the club's values, traditions and history.
"Michael's achievements in leading the club back to the Champions League should not be understated.
"He has forged a strong bond with the players and can be proud of the winning culture at Carrington and in the dressing room, which we are continuing to build."
United end their shortest season in 111 years with a 40th and final match in all competitions away to Brighton in the Premier League on Sunday.
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