The minimum wage in New Jersey is currently $8.85, and raising it to $15 would boost the incomes of more than 1 million people in the state, according to New Jersey Policy Perspective, a liberal-leaning research group. The bill proposes increasing the minimum wage to $10 an hour on July 1. On Jan. 1, it would increase to $11 an hour, and then would increase by $1 an hour every year until it reaches $15 in 2024.

“No one working a full-time job should ever live in poverty,” Mr. Murphy, a Democrat, said in a statement. “Putting the minimum wage on a clear and responsible path to $15 an hour is good for workers, good for our businesses and good for our economy. A higher minimum wage strengthens all of New Jersey.”

The announcement of an agreement between Mr. Murphy, Stephen M. Sweeney, the senate president, and Craig Coughlin, the speaker of the assembly, amounts to a fait accompli; both Mr. Sweeney and Mr. Coughlin had said they would not introduce a bill unless it could pass and Mr. Murphy would sign it. With Democrats in control of both houses of the legislature, passing the bill will be a formality.

The agreement also marks a major political victory for Mr. Murphy, who made raising the minimum wage and legalizing marijuana central promises during his run for governor. Though he said during his campaign that he wanted to raise the minimum wage to $15 by 2021, the governor said he was willing to negotiate with legislative leaders to get it passed early this year.

The bill includes some exceptions: For seasonal workers and employees at small businesses who employ five workers or less, the base minimum wage would reach $15 an hour by 2026. For farmworkers, the base minimum wage would increase to $12.50 an hour by Jan. 1, 2024. Then, a special committee would review whether to raise those workers’ minimum wage to $15 an hour.