The contract is worth $2 million, a source told ESPN.com's Pierre LeBrun.
After the Avs missed the playoffs for a second straight season, the 36-year-old forward was torn about returning for a 14th season.
In the end, Hejduk elected to give it one more shot, especially because he's only nine games away from reaching 1,000 for his career.
The soft-spoken Hejduk was an effective on-ice leader for Colorado this past season. Under his guidance, the Avs improved by 20 points from the year before, when they had the second-to-worst record in the league.
Not only that, but the team saw the rise of forward Gabriel Landeskog, a Swedish standout who is a leading candidate for rookie of the year and led the team with 22 goals.
"I believe in this organization and our young players and look forward to helping the team in any way that I can," Hejduk said. "My family and I are very excited to continue my career here in Denver."
Hejduk ranks fourth in goals (371) and fifth in assists (423) in franchise history.
However, Hejduk's production slipped last season as he finished with just 14 goals. He had scored at least 20 goals in 11 straight seasons heading into 2011-12.
Still, the three-time Olympian has been a reliable part of the Avalanche for more than a decade and remains a fan favorite. He helped the Avs to the Stanley Cup crown in 2001.
"Over the years, Milan has been an instrumental part of our organization's success," general manager Greg Sherman said. "He has represented this franchise with class and will continue to complement the young nucleus of players we have been building this team around."
This was the second big move of the offseason for Colorado. The team also signed coach Joe Sacco to a two-year extension last month.
With their coach and locker-room leader now on board, the Avs will turn their attention toward other matters concerning their roster. Peter Mueller is a restricted free agent, along with defenseman Erik Johnson, leading scorer Ryan O'Reilly and Matt Duchene, who missed a chunk of the season with knee and ankle injuries.
Jamie McGinn and Steve Downie, two players Colorado acquired before the trade deadline, are also restricted free agents. McGinn had 13 points in 17 games since his arrival from San Jose, while Downie was on quite a pace before a shoulder injury slowed him.
Information from The Associated Press was used in this report.