The accord was announced just before midnight Wednesday by unions after two days of talks with officials, and a one-day strike which saw police stations virtually shut as officers carried out only emergency duties.
They have complained of exhausting hours of patrols and chronic under-investment in equipment which have stretched departments to the breaking point and taken a heavy toll on the force.
Last month an officer who led an "angry police movement", which emerged after the 2016 firebombing of a squad car with two officers inside, was found dead at her home in a suspected suicide.
For many officers, the violent clashes with rioting "yellow vest" protesters in Paris and other cities on recent Saturdays, and the huge manhunt for the gunman who attacked a Christmas market in Strasbourg last week, were the final straw.
"This agreement... paves the way for improved and upgraded working conditions and pay for officers," Interior Minister Christophe Castaner said in a statement.
Union officials said that starting next year average monthly pay will be gradually boosted by 120 euros ($137) a month, and up to 150 euros a month for senior ranks.
The government will also begin negotiations on the huge backlog of overtime pay, with unions saying they are owed a collective 275 million euros.
With the pay hikes, the government said a planned 300-euro bonus for officers would now be reserved only for administrative employees and technicians.
"It's what we were looking for, we wanted an immediate boost to spending power," said Yves Lefebvre of the Unite-SGP Police union after Wednesday's talks.
Police were emboldened in their demands after the government announced a 10-billion-euro package of financial relief for low-income households to quell the "yellow vest" protests which have rocked France over the past month.
The measures include a rise in the minimum wage, tax relief for pensioners and tax-free overtime pay for workers.
The total cost of the police pay increases was not disclosed.