Goal.com reported on Thursday night that the 34-year-old midfielder has a tentative agreement in place to join the Galaxy this summer.
Lampard has been the topic of transfer speculation over the past month with Chelsea willing to let the club legend leave this summer.
The England international would replace David Beckham as a big-name England international playing in the Galaxy midfield.
Lampard would be the latest club legend to leave Stamford Bridge with Didier Drogba leaving for Chinese club Shanghai Shenhua this past summer.
The Blues have installed a transfer policy focused on bringing in young players over the past few transfer windows, a policy that has seen Lampard being placed on the bench more often than he is used to this season.
With young talent that includes Ramires, Oscar, Eden Hazard and others in the Chelsea midfield, the Blues have sought midfielders that will be roaming the pitch at Stamford Bridge for years to come as replacements for Lampard.
For Major League Soccer, this is a huge capture for a league that was looking to replace Beckham with a star that was not only a big name, but a player that could thrive in Los Angeles under manager Bruce Arena.
The two-time defending MLS Cup champions add Lampard to a roster that is full of international superstars like Robbie Keane and Landon Donovan.
Lampard has seen a boost in his form of late with five goals in his last six EPL matches, two of those goals came against Everton on December 30.
When Lampard enters the league this summer, he will take the place of Beckham not only as the club's third designated player, but as the club's midfield ace.
For more transfer updates throughout January, stay tuned to Bleacher Report and follow me on Twitter, @JTansey90.