Rowley moves to the King Power Stadium on a one-year deal, following striker Jack Barmby in making the move from Old Trafford.
The 19-year-old has displayed versatility during his time with United, operating in central midfield as well as in his normal role of left-back.
He will now continue his progression with Leicester's development squad after becoming their fifth signing of the close-season.
In addition to Barmby and Rowley, Leicester have also brought in goalkeeper Ben Hamer, centre-back Matthew Upson and midfielder Marc Albrighton.
Nigel Pearson's men start their campaign at home to Everton on August 16.
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