Shawcross, 33, spent 14 years at Stoke making more than 400 appearances for the club, the majority of them in the Premier League.
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He was named Stoke captain for the 2010-11 season, and led the team out in the 1-0 FA Cup final defeat against Manchester City in 2011.
"Ryan fits the Inter Miami DNA because of his experience and his longevity at a club," Inter Miami sporting director Chris Henderson told the club's website.
"He is going to be able to come here and be a leader, not only on the field, but his leadership will be seen with the young players and players coming through."
Shawcross was a key member of the Stoke team that finished ninth in three successive Premier League campaigns but he has struggled for minutes since breaking his leg in a preseason friendly against Leicester in 2019.
The central defender will link up with new Inter Miami coach Phil Neville following his appointment last month.
"He's physically dominant, his feet are good, his range of passing is good and we think he's going to be a great addition to our backline," Henderson added.
"Adding another central defender was important for our group and we want to create competition at every position. That's the goal, to be able to go out everyday and the players are fighting for their spot. That will help the team as a whole. That's Phil's vision to have competition."
They have also re-signed veteran midfielder Federico Higuain to a new contract for 2021.