The council gave general approval to the agreement and is scheduled to vote on it Jan. 27.
Members of the American Federation of State, County and Municipal Employees Local 3373 also will vote on whether to accept the contract. Union negotiator James Bestpitch said he expected members would approve it.
Under the contract, the union members would get a 4.4 percent pay increase in February and an additional 2.5 percent pay increase - as is proposed for all city employees - in July.
"I am pretty relieved," Patrol Officer Wayne Hose, president of the police union, said after the discussion. "I am pretty satisfied with what we got."
"I want to thank you," Bestpitch said. "It has been contentious. We have been at each other's throats."
The police union's contract expired in June 2001, but the city has honored the terms of the original contract, Budesky said.
The two sides had been unable to agree on a wage increase, so police union members have not had a pay raise in three years, city officials said.
While the city has worked out contracts with three of the four unionized employee groups in the last 18 months, attempts to reach a compromise with the police group of about 80 members had been unsuccessful.
Going into Tuesday's work session, the city was asking for an 18-month contract with the union, while the union was asking for a 21/2-year contract.
At one point Tuesday, Councilman Lewis C. Metzner suggested the union consider accepting, immediately, a six-month settlement while the two parties try to work out their differences for the next fiscal year.
Hose and Bestpitch indicated they were not interested in doing that.
When an 18-month contract compromise was proposed, however, they asked for a break. Union members talked in the hallway while the council moved onto other items on the work session agenda.
At its Dec. 11 meeting, Hagerstown's mayor and City Council began public negotiations as the two sides exchanged offers.
City officials wanted the union to accept a reduction in the sick leave buy-back program or face not getting a 2.5-percent pay raise.
The union's counteroffer included a stipulation that only union members with at least 800 sick-leave hours could sell their sick leave back to the city. Under that plan, eligible members could sell back up to 40 hours per year.
Either proposal would have saved the city about $18,000 for the fiscal year starting July 1, Budesky said.
The compromise reached Tuesday includes the union's proposed change to the sick leave buy-back program and the union's proposed pay scale.