Council members Curren Price and Katy Yaroslavsky were absent during the vote.
The provision regarding re-employment is expected to assist some 86 workers who were fired for non-compliance with the policy.
Department management would handle the hiring process, as usual.
A health care worker prepares a dose of Covid vaccine for injectionGetty Images
The city of Los Angeles withdrew its declaration of emergency pertaining to Covid in February 2023.
In May 2023, the federal government also declared an end to the Covid public health emergency.
City leaders wanted to proceed with caution before ending the requirement, he added.
City News Service contributed to this report.