The contract is worth $29.5 million total, for an average annual value of $5.9 million a year, a source told ESPN.com's Pierre LeBrun.
The 25-year-old Varlamov is thriving under first-year coach and Hall of Fame goaltender Patrick Roy, posting a 26-9-5 record with a 2.43 goals-against average. He's second in the league in saves (1,199) this season and his 26 wins already match a career high.
Joe Sakic, the team's executive vice president of hockey operations, says that Varlamov is "entering the prime years of his career and he wants to be part of this franchise moving forward. We are very excited to have come to terms with him."
Varlamov was a first-round pick by Washington before being acquired by Colorado on July 1, 2011.
He will represent Russia at the Sochi Olympics next month.
Information from The Associated Press was used in this report.