Steffen, a backup at City, made 21 appearances for the Premier League club over four seasons, with most of his game time coming in cup competitions.
The 28-year-old spent spells on loan with German club Fortuna Dusseldorf and English Championship club Middlesbrough.
Steffen has made 29 appearances for the United States and will be hoping that regular football back home could help him win back a starting place ahead of the 2026 World Cup, which the USA is co-hosting with Mexico and Canada.
"We are incredibly happy to bring Zack to the club. He is a top player with big experiences and we know he will add so much to our group. His quality, leadership and winning mentality will help us for years to come," said Rapids head coach Chris Armas.
Steffen made his name in MLS for Columbus Crew and was voted MLS Goalkeeper of the Year in 2018.
The Rapids finished 28th in the overall standings for the 29-team last year and Armas was appointed as the new head coach in November.
