Reports emerged on Sunday (AEST) that Bale, who had been linked with a switch to hometown club Cardiff City, had agreed a deal to move to California.
The official website of MLS claimed the winger was to join LAFC on a one-year contract using targeted allocation money.
That deal has now been confirmed by Bale himself, with the 32-year-old posting a video to his official Twitter account.
The clip was captioned with the post "see you soon, Los Angeles" and showed Bale, who appeared to be standing on a golf course, wearing an LAFC jersey and baseball cap.
Bale's Real Madrid contract expires this month and he had had been looking for a new club since guiding Wales to qualification for the 2022 FIFA World Cup.
Wales faces United States in its first group-stage match at the FIFA World Cup in Qatar later this year.
Before then, Bale's signing boosts an LAFC team which already leads the Supporters' Shield race and has also secured Italy defender Giorgio Chiellini ahead of the transfer window in MLS opening next month.
LAFC's first match after that date is El Trafico against rivals the LA Galaxy.