United have not yet disclosed the fee for the 26-year-old but it is believed to be in the region of £17m.
Hargreaves has agreed personal terms and passed a medical so now he only has to officially put pen to paper on what is expected to be a five-year deal.
"Owen will formally sign his contract when he returns from a holiday at the end of June," read a United statement.
Hargreaves, who is taking a family break in his native Canada, has been a long-time target for United.
United chief executive David Gill told MUTV: "It is no secret that we tried to get Owen last summer. We tried again in January but to no avail.
"Thankfully, we have managed to secure him now and we are delighted with that.
"It is good business for us, good business for Bayern Munich and good business for Owen. He is a great signing."
Hargreaves enjoyed an illustrious 10 seasons at Bayern, winning six league titles and the 2001 Champions League.
But his final season was plagued by injury and ended with Bayern finishing fourth in the Bundesliga, thereby missing out on Champions League qualification.
Hargreaves had a four-month lay-off at the start of the campaign because of a broken leg and went on to play in only nine league games.
He will also miss England's matches against Brazil and Estonia in June because of a knee problem.
The announcement of Hargreaves' arrival at Old Trafford comes less than 24 hours after it was revealed that United had agreed "in principle" to sign Brazilian midfielder Anderson, 19, from FC Porto and Portuguese winger Nani, 20, from Sporting Lisbon.
The deal for the duo could amount to a total of £30m.
And Gill hinted that could be the end of the club's summer signings, saying: "We will see what happens over the next two or three months but by and large that will be the major element of our business.
"If a player comes up that Sir Alex is convinced will make us better, I am sure we will find the funds but that is a major bit of business we have done this week."
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