Owen has won 89 caps and scored 40 goals for his country, although he has not played internationally since 2008.
He spent three seasons at Manchester United but played in only 52 games, netting 17 times. He made just four appearances for the club last season.
Owen said he was "particularly excited" at the prospect of working under Stoke manager Tony Pulis.
"He has assembled a great squad that I look forward to joining," said Owen. "I'm now looking forward to contributing as much as possible to the club and can't wait to play in front of a great set of supporters."
He added: "We have been in talks for a while and it was a club I was always keen to join."
Liverpool dismissed suggestions they were keen to bring Owen back to Anfield. Everton and Sunderland also distanced themselves from reports they had attempted to sign the player during the summer.
Michael Owen's career stats
297 games, 158 goals
40 games, 14 goals
79 games, 30 goals
52 games, 17 goals
89 caps, 40 goals
Owen's career has been blighted by injury problems and he has not played a competitive game since November because of a thigh problem. He has started just one Premier League game in the last two seasons.
Owen recently admitted to frustration at the limited opportunities given to him during his time working under Sir Alex Ferguson, but denied suggestions that his time playing in the top flight may have passed or that he was considering retiring from the game.
Owen, who has been staying fit using a personal programme designed by the Manchester United coaches, becomes Stoke's seventh signing of the summer, following the arrivals of Jamie Ness, Geoff Cameron, Michael Kightly, Maurice Edu, Charlie Adam and Steven N'Zonzi.
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