The deal will have Rodriguez stay through the conclusion of Almeria's 2020-21 campagin in May and could become permanent.
"Brian is joining Almeria as they make a strong push for promotion to Spain's top division," said LAFC co-president and general manager John Thorrington. "Since his arrival in 2019, Brian has been a focal point of our attack and a huge reason for our success. This move gives him a great opportunity to play important games at the highest levels of European football."
Rodriguez, 20, joined the Major League Soccer side in 2019 from Uruguay side Penarol. In his first two seasons in Los Angeles, Rodriguez scored three goals in 25 appearances.
He has three goals in nine appearances for Uruguay, appearing for La Celeste during their most recent CONMEBOL World Cup qualifying matches.
With 16 games remaining, Almería currently sits in third place in LaLiga 2 standings with a 14-3-5 record (45 points). At the conclusion of the season, the top two teams will earn automatic promotion to Spain's top division, while a third team earns promotion from a playoff bracket between the teams that finish from 3rd to 6th.
LAFC also announced the signing of 20-year-old goalkeeper Tomas Romero.