Andersen's attorney, Mark Bryant, confirmed the agreement on Wednesday, saying it could be signed later in the day. The deal was first reported by the Denver Post.
Andersen, who turned 31 on Tuesday, could make up to $26 million over the lifetime of a back-loaded contract that gives the Nuggets financial flexibility.
The Nuggets didn't return phone calls.
Andersen will make close to $3.65 million in 2009-10, up from the $998,398 he made last season, when he averaged 6.4 points and 2.5 blocks in 20.6 minutes.
"You write the best-case scenario, think you're dreaming and open your eyes and it's real," Bryant said. "He's very excited. They treated him as a priority."
With his colorful tattoos and spiky hair, Andersen was an instant hit with Denver fans, who've embraced his return to the court.
Andersen came back to the NBA in 2008 following a ban that lasted almost two years after he tested positive for an undisclosed "drug of abuse."
The energetic forward known for his defensive disruption around the basket provided a spark off the bench as the Nuggets made a run to the Western Conference finals, where they fell to the Los Angeles Lakers in six games.
Andersen began his career in Denver in 2001, before bolting to New Orleans three seasons later. He had a breakout season with the Hornets in 2004-05, only to have his career derailed by drugs.
Following his ban, Andersen returned to New Orleans late in the 2007-08 season, playing five games and blocking four shots.
Several teams offered him NBA minimum contracts before the 2008 season, but he elected to play in Denver, where he lives.
Andersen replaced Marcus Camby's shot-blocking presence in the middle, adding a big dose of energy as well -- swooping his arms after big plays.
The fans ate it up. Some of Andersen's flock would even arrive at Pepsi Center wearing feathery costumes and spiky hair.
Andersen received a raucous ovation whenever he entered the game.
"They've really embraced him," Bryant said of his legion of fans. "I think it's a win-win [situation]. They [the Nuggets] wanted him and he wanted to be here."