Son joins an LAFC side currently sixth in the Western Conference and reunites with former Tottenham team-mate Hugo Lloris.
He made his final appearance for Tottenham in a 1-1 pre-season friendly against Newcastle in Seoul, South Korea, on Sunday.
After arriving from Bayer Leverkusen in 2015 he scored 173 goals in 454 appearances for Spurs.
He was captain when Tottenham beat Manchester United in the Europa League final in May to clinch their first trophy in 17 years.
Tottenham chairman Daniel Levy said: “Sonny is one of the greatest players to ever wear the famous Lilywhite shirt and he has been a joy to watch over the past decade.
“Not only is he a wonderfully gifted footballer, but he’s also an incredible human being who has touched hearts and inspired people throughout the club and all over the world.
“Sonny has given so much to this club, both on and off the pitch, and for that we are forever grateful.
“We wish him all the best for the future, and he will always be welcome back at the club as a beloved and cherished member of our Spurs family.”
