Boston utility NStar has agreed to pay a starting price for power from the Cape Wind project that is substantially above the cost of conventional energy and will slightly increase the average customer’s monthly bill beginning the first year the offshore wind farm generates electricity, according to a 15-year contract filed with state regulators Friday.

The price, 18.7 cents per kilowatt hour, is the same as what National Grid agreed to pay when it signed a contract in 2010 to purchase half the power generated by Cape Wind. NStar’s deal is to purchase 27.5 percent of the wind farm’s total output. Since the Cape Wind power represents only about 2 percent of the energy distributed by NStar, it is expected to have a moderate impact on the average customer’s bill, $1.08 a month. Customers in the Boston area pay about $86 a month.

Cape Wind executives and advocates believe the project will, in the long run, help moderate regional energy costs.

The $1.6 billion contract still needs the approval of the Massachusetts Department of Public Utilities. NStar, with 1.1 million electric customers, has asked for a decision by the end of the year.

The utilities currently pay about 8 cents per kilowatt hour for electricity, and NStar originally balked at becoming a Cape Wind customer, arguing the wind farm’s cost was too high. That position changed last month, when, after nearly a year of negotiations, state energy officials agreed to endorse a proposed merger between NStar and Connecticut-based Northeast Utilities if NStar made several concessions, including buying power from Cape Wind.

“We know that it will take a diversified approach using all available renewable resources to meet the state’s climate change goals,’’ NStar spokeswoman Caroline Pretyman said. “We recognize that renewable energy has a cost associated with it but we see this as an investment in our state’s clean energy future.’’