Mastroeni made 230 appearances for the Rapids in an 11-year stay at the Denver-based side, winning the 2010 MLS Cup.
The 37-year-old had been in temporary charge over pre-season following Oscar Pareja's departure in January, but has now been given the reins on a full-time basis.
"It is a great honour to take this new position at the Rapids, a club which means a great deal to me and my family," Mastroeni told the official franchise website.
"I would like to thank the Kroenke family, (president) Tim Hinchey and (technical director) Paul Bravo for this great opportunity.
"I have seen this team's ability and potential up close over the last two months, and I can't wait for the season to get started."
Mastroeni made 65 appearances for the United States in a distinguished career and will be charged with improving on last season's elimination from the first stage of the play-offs.
"For a long time, Pablo Mastroeni has been an icon and a leader at this club, and he has the respect of everyone here, from the players through to the staff," Bravo added.
"He is committed to this club and our project, and I look forward to working closely with him in his new position."
Colorado's MLS season gets under way with a trip to New York Red Bulls next Saturday.
