Doyle's deal is pending his visa, international transfer certificate and medical, while terms of the contract were not disclosed as he joins Gabriel Torres and Juan Ramirez as designated players in Colorado.
The 31-year-old's move to the United States ends his five-year association with Wolves, where he scored 30 league goals in 160 appearances since 2009.
"I am delighted and very excited to be moving to the Colorado Rapids," Doyle told the Rapids' official website.
"With so many great players moving to MLS to join up with the great American talent already there, it's a great time to play in this league.
"Sporting Director Padraig Smith, President Tim Hinchey, along with Technical Director Paul Bravo and Head Coach Pablo Mastroeni have impressed me with their ambition and vision for the club. And Colorado is a great place to bring up a family."
Doyle, who has amassed 61 caps and 14 goals for Republic of Ireland, joins international team-mate Robbie Keane (Los Angeles Galaxy) in the MLS.
"I know from talking to Robbie Keane that MLS is a great league to play in and I look forward to being another top Irish player there," Doyle added.
"I will be sad to leave Wolves, a truly great club that I've had the privilege to play for. I will always be grateful to the fans for their support; it is they who make Molineux such a special place.
"To be involved in the current squad that is on an exciting run is now my only focus, as it would mean so much to me to see us get back to the Premier League."
The Rapids play host to expansion club New York City on Saturday.
