LAFC announced the move made with targeted allocation money on Monday.
Ginella already has spent three seasons in Uruguay’s first division with Montevideo Wanderers, making his pro debut in April 2018.
He played alongside Rodriguez at the U20 World Cup in Poland last summer.
LAFC is preparing for its third MLS season after winning the Supporters’ Shield earlier this year as the league’s regular season champions in just its second season of existence. LAFC then lost to Seattle in the Western Conference playoff final.