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.
Owen will be reunited with striker Wayne Rooney whom he successfully partnered in attack for England before injuries curtailed his international career.
"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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