The 16-year-old has been linked with a number of Premier League sides, including Liverpool, but City won the race for the youngster.
“They have come up with a deal which is good for all parties,” Swindon chairman Andrew Fitton said.
“We’ve been approached by a number of Premier League sides and that includes a discussion with Liverpool.”
“Part of the deal is an understanding about what we might do together in the future and a first refusal on him coming out on loan to us,” he added.
“He’s a special talent but he’s also young so he’s got a lot of learning to do.”
