The deal is worth about $58 million over four years, the Los Angeles Times reported, citing sources familiar with the negotiations.
The deal would keep Bynum under contract with the Lakers through the 2012-13 season, according to the report. The first three years of the deal are reportedly worth nearly $42 million, with a team option fourth year for about $16 million.
"We're extremely happy to have signed Andrew to this extension, which will secure his immediate future with the franchise," Lakers general manager Mitch Kupchak said in a statement. "Andrew has shown a vast array of skills for a player his size and if he continues to stay dedicated and work hard to improve, he has an excellent chance to develop into one of the top players in the NBA."
Bynum, the 10th overall pick in the 2005 draft, will make $2.8 million this season. If an agreement hadn't been reached by Friday, the Lakers wouldn't have been able to negotiate with him until after the season and he would have become an unrestricted free agent.
"This has been a fantastic week for me so far: turning 21, winning our first two games of the season, and now getting this new contract signed," Bynum said. "This gives me and my family financial security, and more importantly, cements my future with the Lakers, which in my opinion is the best organization in all of professional sports. I couldn't be happier."
Bynum, a 7-foot, 285-pounder, established himself as one of the NBA's up-and-coming big men last season before having season-ending knee surgery Jan. 13. He averaged 13.1 points, 10.2 rebounds and 2.06 blocked shots in 35 games, 25 of them starts, before being injured.
The Lakers reached the NBA Finals without him, losing to the Boston Celtics in six games.
Bynum appears healthy now, making his team a solid favorite to win its first championship since 2002. He's averaging 7.2 points, 5.6 rebounds and 1.3 blocks in his career.
Bynum became the youngest player to be drafted in NBA history when the Lakers selected him following his graduation from St. Joseph High School in Metuchen, N.J.
Information from The Associated Press was used in this report.