"Michael is a world class forward with a proven goalscoring record at the highest level and that has never been in question," said manager Alex Ferguson.
"Coming to Manchester United with the expectations that we have is something that Michael will relish," he added on the club's official website.
Owen, 29, had been out of contract after deciding to leave relegated Newcastle United and becomes Alex Ferguson's second signing of the close-season following Ecuador winger Antonio Valencia's move from Wigan Athletic on Tuesday.
"I had just begun to talk to other clubs when out of the blue Sir Alex phoned me on Wednesday afternoon, invited me to have breakfast with him next morning during which he told me that he wanted to sign me," Owen said. "I agreed without a moment's thought."
He had a single season at the Bernabeu where he failed to hold down a first team place amongst the "galacticos", before moving on to Newcastle in 2005 who were relegated to the Championship (second division) in May.
"I am now looking forward to being a Manchester United player and I am fortunate that I already know so many of the players here," Owen added.
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