Sources close to the deal have told Goal that the Galaxy will pay a fee of €9 million (£8m/$10m) plus €3m in bonuses to land the Mexico star.
That outlay will break the Galaxy's previous club-record fee of $7m, which they spent to acquire Hernandez's international team-mate Giovani dos Santos in 2015.
Long linked with a move to MLS, Hernandez is finally set to play in the North American top flight after only signing with Sevilla in September from West Ham.
Hernandez has previously turned down the chance to move to MLS but his lack of minutes with Sevilla has helped convince him that the time is right to return to North America.
The 31-year-old has made 15 total appearances with Sevilla this season, starting nine games and scoring one goal.
For their part Sevilla are happy to sell, as their potential return of €12m would mark a solid profit after they spent €8m to sign him from the Hammers.
Hernandez will head to a Galaxy side that is looking to help fill the void left by Zlatan Ibrahimovic, who departed the club at the end of the 2019 season and has since signed for AC Milan.
The move will be seen as a major coup for MLS, which should see an increase in attention at home with the addition of one of the most popular Mexican players of his generation.
Hernandez is Mexico's all-time leading scorer, netting 52 times in 109 appearances with El Tri.
For the forward, the move will mark the end of a 10-year adventure in Europe that began when he joined Manchester United from hometown club Chivas de Guadalajara in 2010.
The striker played five seasons with the Red Devils, scoring 59 goals and winning two Premier League titles.
Hernandez found his scoring touch in Germany as he scored 28 league goals in just two seasons before moving to the Premier League with West Ham.
In the Premier League, Hernandez scored 16 times in just over two seasons with the Hammers.