The council's 12-0 vote set the stage for city leaders to later consider binding agreements with developer Anschutz Entertainment Group on the project's financing, leasing arrangements and other details.
"This is not the beginning of the end but perhaps the end of the beginning," Councilman Eric Garcetti said before the vote was taken.
The agreement anticipates the issuance of $275 million in tax-exempt bonds for the relocation of a convention center hall to accommodate the proposed $1.2 billion football venue.
It would require AEG to extend a series of financial guarantees over the course of the project as a safeguard against shortfalls and other risks.
The council vote gives AEG officials the solid demonstration of city support that they said they needed in order to ramp up their efforts to secure a team at the planned stadium known as Farmers Field.
"It sends a very strong message to the league now," AEG president and CEO Tim Leiweke said at a news conference after the vote.
NFL spokesman Brian McCarthy said in a statement after the vote that the league was aware of the council vote and would continue to monitor all stadium developments in the Los Angeles area.
Sports management mogul Casey Wasserman, an early collaborator with AEG on the stadium proposal, praised the council's decision in a statement.
"This is a long process, but today marks a step forward in reaching our larger goal," he said.
The firm's stadium plan is one of two competing proposals to bring professional football back to Los Angeles some 16 years after the Rams and Raiders left the nation's second-largest market.
Warehouse magnate Ed Roski's Majestic Realty Co., which also has not yet secured a team, has permits in place to build a separate 75,000-seat stadium about 15 miles east of Los Angeles, in the city of Industry.
John Semcken, a Majestic vice president, said in a statement after the vote that its proposal would generate more money and jobs and be a better choice for the NFL.
"We are more active than ever and are currently working with the league, owners and teams to bring a franchise back to Los Angeles," he said.
The Los Angeles council members are set to take up the additional binding votes over the next nine months, with groundbreaking on the new venue possible as early as June.
Council members would still have a chance to ask AEG to help fund stadium infrastructure, such as its transit connections, and to establish job training programs as the binding agreements are considered, said Chief Legislative Analyst Gerry Miller, who led the city team that negotiated the framework deal.
"Until those final terms are accepted, you can change them," he said.