The 32-year-old will join on a one-year contract, having left Real Madrid this summer.
Bale was reportedly in discussions with Cardiff City but the move has not materialised.
The former Southampton youngster was forced to quash rumours of a move to Getafe earlier this month after the club's president claimed he had been offered the chance to sign the Wales captain.
Bale is keen to maintain fitness for the upcoming FIFA World Cup in Qatar later this year, where Wales have been placed in the same group with England, Iran and USA.
Bale is the second high profile signing to be joining LAFC this summer after former Italy international Giorgio Chiellini also joined the club on a free transfer.
Bale confirmed the move on his social media pages, saying: "See you soon, Los Angeles". It was accompanied by a video of Bale in a LAFC hat.
A then world record fee of £85m exchanged hands when the Welshman transferred from Tottenham Hotspurs to Real Madrid in the summer of 2013.
His list of laurels at the Bernabeu included five Champions League titles, three La Liga trophies, one Copa del Rey, three UEFA Super Cups and three FIFA Club World Cups.
