Domingo said he did so "with a heavy heart," the LA Times reported.
"Recent accusations that have been made against me in the press have created an atmosphere in which my ability to serve this company that I so love has been compromised," he was quoted as saying in a statement.
Domingo has led the LA Opera since 2003. The company said in a statement that the star performed more than 300 times in 31 different roles.
The resignation came a week after Domingo withdrew at the last minute from a run of performances of "Macbeth" at the New York Metropolitan Opera, and after a number of other US arts organizations cancelled his appearances.
Several female singers and one dancer have accused the Spanish singer of unwanted kisses, hugs, nightly telephone calls and of pressuring them to meet him privately. Domingo has rejected their accounts as "inaccurate."
The scandal surrounding the popular opera performer, a tenor for most of his career who now sings mainly baritone parts, has divided fans and cultural institutions.
In the US, the San Francisco Opera and the Philadelphia Orchestra cancelled concerts planned for Domingo; while at the Salzburg Festival in Austria in August, he received a standing ovation in his first performance since the damaging claims emerged.
----------------------------------------------------------------------------------------------------------------