New England janitors involved in a contract dispute that led them to the brink of a strike voted to ratify a new contract on Saturday, overwhelmingly approving an agreement that increases the number of full-time jobs, boosts wages, and establishes a four-hour minimum shift.

A major demand of the 14,000 workers represented by the Service Employees International Union Local 615 was more full-time jobs — and the benefits that go with them. The four-year agreement with the Maintenance Contractors of New England raises the number of full-time posts by at least 680 — to more than 5,200 in Greater Boston. Currently, two-thirds of union members work fewer than the 30 hours a week required for health insurance.