Sporting KC received $200,000 in general allocation money and $200,000 in targeted allocation money in exchange for the 32-year-old playmaker.
The UCLA product will return to Southern California and reunite with former U.S. national team coach Bob Bradley, who selected him to play in the 2010 World Cup.
"Benny and I shared some good days with the U.S. national team," Bradley said in a news release. "I am excited to work with him again. He has an attacking quality and an excellent understanding of the game."
Feilhaber joins LAFC after five seasons with Sporting KC, during which he compiled 29 goals and 43 assists in 157 MLS matches.
An MVP finalist and Best XI selection in 2015, Feilhaber helped Sporting KC win the 2013 MLS Cup title as well as the U.S. Open Cup in 2015 and 2017. He has earned 44 caps for the U.S. national team, including three in 2017 after a three-year absence from the program.
"Benny has been a really good player for our organization since 2013 and we appreciate his contribution to the club," Sporting KC coach Peter Vermes said. "On a personal note, I am very happy that I was able to coach Benny twice, both here and with the U-20 national team, and we wish him nothing but the best."
Feilhaber, who also has played for Hamburg, Derby County, Aarhus and the New England Revolution, departs after Kansas City signed French attacking midfielder Yohan Croizet as a designated player last month.
He joins an LAFC squad that now features goalkeeper Tyler Miller; defenders Laurent Ciman, Walker Zimmerman, Omar Gaber and Jordan Harvey; midfielder Rodrigo Pacheco; and forwards Carlos Vela, Diego Rossi, Marco Urena and Latif Blessing.
The expansion side also possesses the No. 1 overall pick in the MLS draft, which will be held Jan. 19 in Philadelphia.