Outgoing Chief William Bratton has been an opponent of the idea, but his resignation takes effect in three weeks. The mayor, surrounded by police commanders, announced the compromise over police hiring on Monday.
"The city faces far too many challenges far right now for the mayor and the council to distract ourselves with a battle over cops," said Mayor Villaraigosa.
The LAPD is 37 officers short of the 10,000 that have been the mayor's goal. It's more officers than when then mayor took over, and the numbers are given credit for record low violent crime rates.
"Why is it better? Because we have more resources, we have more flexibility, we're able to do operations that dig to the heart of the issue," said Dep. Chief Charlie Beck.
Homicides are down 16 percent from last year.
Bratton has argued against any proposals to halt hiring and suspend recruiting efforts, saying it could result in the LAPD having 300 fewer police officers by June.
The mayor had been his most vocal supporter, but on Monday Villaraigosa bowed to a more than $400 million deficit.
"The enormity of this crisis means that we cannot continue to expand the police department at the same rapid pace," said Villaraigosa.
Councilman Dennis Zine, a 40-year veteran of the LAPD, supports the deal, as well as Los Angeles City Council President Eric Garcetti.
"This year we all agreed 9,963 officers, we would not go backwards one bit this year even in a tough budget year," said Garcetti.
The city council was supposed to debate a police hiring freeze and hear from the outgoing chief at a meeting on Tuesday, but it has now been postponed indefinitely.
Bratton is stepping down on Oct. 31 to join a private security firm in New York.
Aside from the hiring freeze, the city is negotiating with the Los Angeles Police Protective League to try to secure concessions to reduce its budget deficit. If no deal is reached, the city will consider 18-day furloughs for officers this fiscal year.