The 18-year-old moves to the Swansea.com Stadium for the next stage of his development, where he will test himself in the Championship in what is the first loan move of his senior career.
It comes after Burns signed a new long-term contract at Manchester City, with the centre-back committing his future to the Club until the summer of 2027 earlier this month.
A tall, imposing defender, who is comfortable in possession, the teenager made his first team debut in September, playing the entire 90 minutes as a youthful City side beat Wycombe Wanderers 6-1 in the Carabao Cup third round.
Having joined the Club as a 13-year-old, Burns progressed through the Academy ranks and helped the Under-18s win the 2020 FA Youth Cup before moving up to the Elite Development Squad (EDS), where he was a key figure in our 2020-21 Premier League 2 triumph.
He has made 22 appearances for the EDS this season, helping Brian Barry-Murphy’s side to the top of the table after 18 games and joins a Swansea side sitting 17th in the second tier.
Everyone at Manchester City wishes Finley all the best during his loan spell.