The Airport Commission approved the pickup plan last month but the City Council asserted its authority and placed the process on hold while it looked into passenger safety issues.
The council on Tuesday voted to ask the California Public Utilities Commission, which regulates ride-hailing firms, to require driver fingerprinting as part of its background checks and told the city attorney to look into whether Los Angeles could also require prints.
"Hardly anyone hitchhikes anymore because of the danger of getting into a stranger's car, but as soon as that stranger responds to us over our smartphone, suddenly that becomes a safe thing?" Councilman Paul Krekorian argued. "No it isn't — not without a fingerprint-based background check."
Councilman Bob Blumenfield said in a statement that the panel had "embraced rather than hindered new technologies to provide the safe and convenient access Angelenos demand."
It was unclear how fast individual ride-hailing companies could obtain city permission to begin making airport pickups, but an Uber spokesman suggested it could happen quickly.
"Angelenos have shown their clear support for more reliable, affordable transportation options" and the company hopes to provide it in the coming weeks, Uber spokesman Michael Amodeo said in a statement.
The vote on driver background checks was praised as a first step to protecting consumers in a statement from William Rouse, general manager of Los Angeles Yellow Cab.
Last week, San Francisco's district attorney announced the expansion of a consumer-protection lawsuit aimed at Uber's contention that it rigorously checks its drivers' backgrounds.
The false advertising suit said the company can't make that claim unless the drivers are subject to the same fingerprinting process as taxi drivers and claimed Uber had failed to uncover the criminal records of 25 California drivers, including several registered sex offenders and a convicted murderer.
In a reply, Uber spokeswoman Jessica Santillo said no background check system is flawless and its checks are just as detailed as with taxi drivers.
A similar lawsuit against Lyft was settled last year.
The AP contributed to this report.