"Andy is a player that we have been monitoring for some time and we are delighted to officially welcome him to the Club," said LAFC EVP & general manager John Thorrington.
"His resume, both in MLS and in Europe, speaks for itself and we're confident that his experience and versatility will only complement the group as we begin our return to play."
The 27-year-old Najar has been training with LAFC since February and will join the team in time for next month's MLS is Back Tournament in Orlando, Florida, which will begin on July 8 at the ESPN Wide World of Sports Complex.
The Honduras international was named the top rookie in MLS in 2010 after tallying five goals and one assist in 26 games with D.C. United.
He registered 10 goals and 11 assists in 82 games with D.C. United before departing after the 2012 season to join RSC Anderlecht in the Belgian Pro League. He scored a total of 14 goals and added 16 assists in 164 matches in Belgium, including seven Champions League and 20 Europa League appearances.
Najar won two league titles and the Belgian Super Cup three times and has also scored four goals in 36 appearances for Honduras since making his national team debut in 2011.