The 32-year-old has departed Real Madrid as a free agent this summer, and he has been strongly linked with a move to Cardiff City ahead of the 2022 World Cup.
However, Bale posted "see you soon, Los Angeles" on his official Twitter account on Saturday, confirming that he is making the move to the North American outfit.
Los Angeles FC are yet to officially announce the deal, although their Twitter account retweeted Bale's post.
The Wales international is believed to have agreed a one-year contract with the MLS outfit, and he will follow legendary centre-back Giorgio Chiellini to the club, with the Italian running down his contract at Juventus before making the move to Los Angeles.
Bale would allegedly have considered retiring from professional football if Wales missed out on qualification for the World Cup, but Rob Page's side beat Ukraine in a playoff to secure their spot in the 2022 competition.
The MLS season runs from February until October, and LAFC will be bidding to make the season-ending MLS Cup final, which takes place 16 days before Wales begin their World Cup campaign against USA.
Bale only made seven appearances for Real Madrid during the 2021-22 campaign, scoring just once during a disappointing final season in the Spanish capital.
The forward has played an important role in the club's success in recent years, leaving with a record of 106 goals and 67 assists in 258 appearances in all competitions.
Bale won three La Liga titles, one Copa del Rey and five Champions League titles during his time in the Spanish capital, but he has had a difficult relationship with the club's fans over the last couple of years.
LAFC are currently top of the MLS Western Conference, picking up 30 points from their opening 15 matches courtesy of a record of nine wins, three draws and three defeats.
The Los Angeles outfit, who are likely to confirm the deal on Sunday, played out a 1-1 draw with Seattle Sounders in their last game on June 18.
"We are all very excited, we weren't necessarily expecting it but transfer windows have the added excitement that you never know what's going to happen so it's definitely exciting to have someone of Bale's calibre and we are excited to welcome him to Los Angeles," LAFC's 3252 Supporters Union president Kristian Garcia told Sky Sports News.
Bale has a record of 183 goals and 139 assists in 540 appearances for Southampton, Tottenham Hotspur and Real Madrid during his professional career.