The city had reached tentative agreements with the unions on Monday for 10 percent reductions in total compensation, said Michelle McGurk, a spokeswoman for San Jose Mayor Chuck Reed.
In a statement, Reed said funds from the concessions would help save library hours, community centers, park rangers, the anti-graffiti program and other services.
"These agreements allow us to move forward, but they do not solve our budget problems," Reed said. "Even with the concessions made to date, we still face hundreds of layoffs and substantial reductions in services in the new fiscal year and a $40 million shortfall in 2011-2012."
The five unions whose agreements were approved today are the City Association of Management Personnel, which represents senior analysts and program managers; the International Brotherhood of Electrical Workers; the Association of Engineers and Architects; the Association of Maintenance Supervisory Personnel, representing building maintenance superintendents and building services supervisors; and the International Union of Operating Engineers, which represents maintenance assistants, park rangers and parking and traffic control officers.
Last week, the city reached an agreement with the Association of Legal Professionals that called for 10 percent concessions in total compensation from the union, which represents 46 public attorneys.
The council twice deferred making a decision on whether to impose a 10 percent cut in wages and benefits on employees or to accept a last-minute proposal brought forward by the remaining five unions last week after union representatives asked for more time to allow negotiators to review their proposal.
The unions had offered a proposal equal to a 10 percent concession in total compensation that met the city's demands, but their offer was initially rejected due to legal issues because it included a provision contrary to the city charter.