Lloris, whose contract with Spurs was due to expire in June, has signed a one-year deal with an option to extend for 2025 and 2026 after an 11-year stay in London.
"Thank you for your support since day one. It's been a great privilege to be one of you and one of your captains as well," Lloris said in a video posted on Spurs' social media.
"It's the end of the chapter, but you will always be in my heart. Spurs will always be a special place for me and my family. Thank you for all the memories we shared. I wish you the best."
Lloris kept 151 clean sheets in 447 games after joining Spurs from Olympique Lyonnais in 2012 and helped his side reach the 2019 Champions League final which they lost to Liverpool.
The former Tottenham captain made 25 Premier League appearances last season but has not played since the arrival of manager Ange Postecoglou in the close season.
Lloris, crowned a World Cup winner in 2018, retired from international football in January after becoming France's most-capped player with 145 appearances.
"Hugo is arguably the most successful goalkeeper of his generation and a proven winner," said LAFC co-president and General Manager John Thorrington.
"We are incredibly excited that Hugo has chosen LAFC for the next phase of his illustrious career.
"He brings unprecedented leadership experience at the highest levels of football, which we know will greatly benefit our club in our pursuit of more trophies."
MLS Cup runners-up LAFC kick off their league campaign on February 24th when they host Seattle.
