The Wall Street Journal says the pact with the American Guild of Musical Artists calls for 2 percent salary increases for each of the next 3 years. It also includes provisions accommodating the Met's intended introduction of earlier curtain times this fall.
The current contract was to expire Sunday.
Met General Manager Peter Geld told the Journal the contract was fair given "the financial challenges of the Met."
The opera expects a balanced budget this year for the first time since 2004.
The Met is still negotiating with two other unions, those representing musicians and stagehands.
The musicians' contract expires on Sunday; the stagehands have until Sept. 5 to reach a deal.