General manager Mitch Kupchak confirmed last month the Lakers would exercise the option.
Bynum, 24, was named an All-Star for the first time in his seven-year career last season, putting up career bests in points (18.7) and rebounds (11.8) per game, while also being named to the All-NBA second team.
The Lakers had to pick up Bynum's option by June 30 or else the 7-footer would have become a free agent.
It was an expected move by the organization as Bynum became a vital part of the team's success while accomplishing impressive individual feats such as hauling in 30 rebounds against the San Antonio Spurs and registering a triple-double that included 10 blocks in the Lakers' playoff opener against the Denver Nuggets.
For all of Bynum's on-court feats, he also had his share of head-scratching moments, from blowing off a meeting with general manager Mitch Kupchak to launching an ill-advised 3-pointer and only vowing to shoot more of them after head coach Mike Brown benched him for it.
Despite all of that, the Lakers decided Bynum is someone who can continue to anchor the team.
"I think it's pretty obvious how I feel about Andrew Bynum," Lakers vice president of player personnel Jim Buss told the "Mason & Ireland Show" on 710 ESPN last week. "He's an incredible All-Star center, and you can build the future around him."
A source close to Bynum said that the All-Star center and the team have "not yet engaged" in any discussions about a long-term contract extension, but that Bynum's camp "anticipated" those talks to occur sometime this offseason.
Information from The Associated Press was used in this report.