The 20-year-old centre-back has signed a three-year contract and will join the Premier League club's development squad.
Harries told his new club's website: "I am delighted to be here. It is a little hard to leave Coventry, but I am really looking forward to getting going at Swansea.
"My aim in the long term is to play in the Premier League. If I am lucky enough and good enough for the manager to trust me at some stage in the future, that would be a dream come true."
Harries progressed through Coventry's academy and made his first-team debut on the final day of the 2015-16 season.
He made a total of 17 appearances for the Sky Blues as they were relegated from Sky Bet League One last season.