Incentives could push the deal to approximately $43 million, Yahoo! Sports reported. The team had yet to confirm the agreement or terms of the extension.
The 28-year-old Bogut was set to become a free agent after the season but had expressed a desire to remain with the Warriors, who have built a strong nucleus around Stephen Curry.
Bogut, the top pick in the 2005 NBA Draft, has battled injuries the past two seasons that limited him to a combined 42 games. But he returned from an ankle problem to start the final 32 games of the 2012-13 regular season and all 12 Golden State playoff games.
When he was on the court, he averaged 5.8 points and 7.7 rebounds -- well below his career averages of 12.2 points and 9.2 rebounds. In the postseason, he scored 7.2 points and pulled down 10.9 rebounds per game.
Bogut began his career with the Milwaukee Bucks. In March 2012, he was traded to the Warriors as part of a deal involving Monta Ellis.