The 18-year-old, who has represented England at Under-16, Under-17 and Under-19 levels, made his Fulham debut against City in 2014 and made 22 appearances for the London side.
Roberts, a forward or winger, arrives at the Etihad Stadium for a fee reported to be in the region of 11 million pounds.
"Manchester City are delighted to announce the signing of @patrick7roberts from @FulhamFC," the club said on their official twitter feed.
Roberts becomes City's third English signing within the last five days following the arrivals of internationals Raheem Sterling and Fabian Delph as clubs look to adhere to Premier League rules demanding clubs have eight home-grown players.
City, who finished second in the Premier League last season, began the close season with just goalkeepers Joe Hart and Richard Wright and defender Gael Clichy meeting the criteria.
(Reporting By Tom Hayward, editing by Pritha Sarkar)
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