The Norwegian initially stepped in as caretaker boss at Old Trafford in December 2018, replacing Jose Mourinho.
He led the club to a third-place Premier League finish in his first full season in charge. United finished second in the table last season and also reached the final of the Europa League, where they were beaten on penalties by La Liga side Villarreal.
Solskjaer, who spent 11 seasons as a Manchester United player, said the club will go from strength to strength under his stewardship.
“Everyone knows the feeling I have for this club, and I am delighted to have signed this new contract,” he said.
“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.”
United executive vice-chairman Ed Woodward added: “Ole and his staff have worked tirelessly putting the foundations in place for long-term success on the pitch.
“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.
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