A press conference is expected on Friday.
[Ads /]
The expansion MLS franchise is due to begin play in March.
The 28-year-old Vela has been at Real Sociedad in Spain's La Liga since 2011, scoring 72 goals in 230 appearances. He was previously under contract with Arsenal, but went on loan to several clubs.
Real Sociedad confirmed Vela's departure to MLS on its website, but didn't announce his exact destination.
"Real Sociedad and Major League Soccer (MLS) have reached a principle of agreement that will see Carlos Vela transferred to a team in the American league during the winter transfer window," a Sociedad statement said.
According to Marca, the transfer fee would be about 5 million euro, after Sociedad paid 14 million euro to bring him in from Arsenal in 2012.
LAFC still must assemble an entire MLS roster around Vela.
[Ads /]
The LA Galaxy acquired Mexican star Jonathan Dos Santos from Spain's Villarreal last month, teaming him with older brother Giovani, who has been at the Galaxy since 2015.
Vela should appeal to Los Angeles' vast Latino population as LAFC begins its competition for fans with the LA Galaxy, the five-time MLS champions.
LAFC made no secret of its hope to sign a major international star to make a splash in the nation's second-largest city, but was unsuccessful in its pursuit of Javier "Chicharito" Hernandez, who instead went to West Ham. LAFC also pursued midfielder Andres Guardado, who went to Real Betis.
ESPN and The Associated Press contributed to this report.