Bogut, the top overall pick in the 2005 draft, also has $12 million in possible bonuses built into the contract, which was expected to be signed Friday, agent David Bauman said.
The agreement was first reported Wednesday by the Milwaukee Journal Sentinel on its Web site.
Bucks spokesman Dan Smyczek also confirmed Wednesday that there was an agreement on a deal.
"He's thrilled," Bauman told The Associated Press. "He feels like Milwaukee really stepped up and demonstrated to him he's a valued member of this team."
The signing should also silence critics who feel the team hasn't shown a commitment to winning, Bauman said. The hiring of Scott Skiles as coach and the trade for Richard Jefferson demonstrated to Bogut that the team was making a push to be competitive.
"These moves show Andrew this team is committed to winning now," Bauman said.
The extension does not affect the nearly $7 million Bogut is owed for the upcoming season, the final year of his rookie contract.
Despite the Bucks' struggles in the past two seasons, Bogut indicated he wanted to stay with the team.
He played in 78 games last season, averaging 14.3 points and 9.8 rebounds.
Bogut is expected to begin practicing with the Australia Olympic team on Tuesday. Bauman said the center hoped to get an extension completed before then, but he wasn't using that date as a deadline for a deal.
Wednesday was the first day for NBA free agents and players seeking extensions to sign contracts.
ESPN.com's Marc Stein contributed to this report.