St. Clair arrives in Miami after starring for Minnesota United, where he posted 42 clean sheets in 159 matches across all competitions with the Loons since arriving in 2019.
The 28-year-old, a free agent after his contract with Minnesota expired, has 18 appearances for Canada and wants to keep building his case to start at the 2026 World Cup, which will be co-hosted by Canada, the United States, and Mexico.
Inter said he'd been signed through 2026, with an option to extend through June 2027.
Miami continues to strengthen the squad that, under Messi's leadership, will defend the club's first-ever MLS Cup title won in December.
In recent weeks, Inter have acquired Argentine defender Facundo Mura and Spaniard Sergio Reguilon, who will replace the retired Jordi Alba at left back.
Inter have also renewed Uruguayan Luis Suarez for another season and exercised their purchase option for Argentine Rodrigo De Paul.