The United States Under-20 international, who has made 41 appearances for the Rapids, will remain on loan with the MLS club until July 17.
Arsenal then intends to loan the 23-year-old out to a European team for the 2022-2023 campaign to further his development.
The transfer, which remains subject to the completion of regulatory processes, was confirmed by Arsenal and Colorado – both owned by Stan Kroenke – on Tuesday.
Trusty made 33 appearances for the Rapids during the 2021 regular season and led the team for minutes played with 2,970.
The tall centre-back chipped in with one goal and three assists, while also ranking joint-fifth for interceptions in MLS last season with 59.
He played a part in 12 clean sheets to help the Rapids finish top of the Western Conference, but they were beaten by the Portland Timbers in the MLS Cup playoffs.
While he has yet to represent USA at senior level, the Pennsylvania-born defender was part of their roster for this month's training camp in Phoenix.
Colorado general manager Padraig Smith told the club's official website: "Auston is coming off an exceptional season in 2021 in which he played a vital role in helping us finish atop the Western Conference for the first time in our history.
"We remain committed to bringing through the top young players from Colorado and across the United States and to providing them with a platform to flourish, achieve success in MLS and earn the chance to make a move to Europe.
"Auston's outstanding performances caught the eye of several European clubs over the past 12 months and we are privileged to be part of an organisation with the reach and scale of Kroenke Sports Entertainment that allows us to help a player of Auston's potential further his development and career aspirations in Europe."
Arsenal are closing in on another player from MLS, meanwhile, with New England Revolution head coach Bruce Arena confirming last week that the Gunners are in advanced talks to sign goalkeeper Matt Turner.
Turner was voted MLS Goalkeeper of the Year in 2021 after helping the Revs to Supporters' Shield success and has been capped 15 times by USA at senior level.