The 37-year-old has inked a contract extending until the conclusion of the 2024 season, with an option for an additional two years.
Lloris, who amassed 447 appearances during his 11-year tenure at Spurs, currently ranks seventh on their all-time list.
“Spurs will always be a special place for me and all my family,” said the former France international.
“It has been a great privilege to be one of yours and one of your captains for many years and it’s the end of the chapter, but you will be always in my hearts.”
LAFC co-president and general manager John Thorrington described Lloris as “arguably the most successful goalkeeper of his generation and a proven winner”.
Lloris, who joined Tottenham from Lyon in 2012, was appointed captain by former manager Mauricio Pochettino in 2015.
Despite being part of the Tottenham side that reached the 2019 Champions League final, he expressed a desire to leave the club in the summer as he entered the final 12 months of his contract.
Since a 6-1 loss to Newcastle in April, Lloris has not made any appearances and has found himself behind Guglielmo Vicario and Fraser Forster this season.
To bid farewell to the fans, Lloris is set to make an appearance on the pitch at half-time during Sunday’s Premier League match against Bournemouth at the Tottenham Hotspur Stadium (14:00 GMT)