The Norwegian's previous deal was due to run out in 2022, but United have agreed to fresh terms to extend his stay as manager. He has signed a three-year contract with the option of another year.
ESPN previously reported that Solskjaer's future did not depend on lifting a trophy last season, with the club committed to handing him a new deal. United are yet to win any silverware under him.
"Everyone knows the feeling I have for this club, and I am delighted to have signed this new contract," Solskjaer said in a statement. "It is an exciting time for Manchester United, we have built a squad with a good balance of youth and experienced players that are hungry for success.
"I have a fantastic coaching team around me, and we are all ready to take that next step on our journey.
"Manchester United wants to be winning the biggest and best trophies and that's what we are all striving for. We have improved, both on and off the pitch, and that will continue over the coming seasons. I can't wait to get out in front of a packed Old Trafford and get this campaign started."
Solskjaer, 48, took over at Old Trafford -- initially as caretaker following the departure of Jose Mourinho -- in 2018. He was appointed to the role permanently in March 2019 -- signing a three-year contract -- after winning 14 of his first 19 games in charge.
"Ole and his staff have worked tirelessly putting the foundations in place for long-term success on the pitch," executive vice chairman Ed Woodward said.
"The results of that have become increasingly visible over the past two seasons and we are all looking forward to seeing this exciting team develop further in the years ahead.
"What is especially pleasing is the way this progress has been achieved with a blend of young, homegrown talent and top-class recruits, playing attacking football in the best traditions of Manchester United. We are more confident than ever that, under Ole's leadership, we are heading in the right direction."
Solskjaer has won 84 of his 151 games as United boss and led the team to a second-place finish in the Premier League last season as well as the Europa League final, where they lost on penalties to Villarreal after a 1-1 draw.
He scored 126 goals in 366 games as a player for United, winning six Premier League titles and the 1999 Champions League.