Locals 34 and 35, Yale’s two labor unions that together represent over 4,500 employees across the University, voted to approve an early contract agreement Tuesday night, marking what University President Richard Levin said he hopes will be a “new chapter” in Yale’s relations with labor unions.

“This is truly a historic day for Yale University, for the community in which we all live and work,” Levin said. “An extraordinary achievement.”

The new three-year contracts will improve health benefits, increase job security and allow both unions to increase in number. In return, the unions have agreed to alter their wage system over the next three years to save money for the University.

More after the jump.

University administrators and union officials attributed the creation of the early agreement — indicative of a better University-labor relationship — to the Best Practices initiative.

“In the past, everyone would approach us whenever we had difficulties with the University in settling contracts [and say,] ‘You should do something to mend your broken relationship, fix your broken relationship.’ I argue we didn’t have a relationship,” Local 35 President Bob Proto said Tuesday. “That is what happened this time around: We actually developed a relationship. … We talked to each other.