PROVIDENCE — It’s the season for giving, and Mayor David N. Cicilline got a holiday present yesterday from the City of Providence.

But Cicilline should feel a little slighted. The mayor was literally the last on his block — the last, in fact, in the entire city — to get this gift: his big green can.

The city’s Public Works Department yesterday gave the mayor the last of the 60,000 trash cans that are meant to dramatically improve trash pickup across the city.

No more cans with the lids blown off, trash blowing into the street. No more bags piled up in heaps on the curb. And residents hope, no more rats.

One of the objectives of introducing the 95-gallon, wheeled, lidded trash cans is to combat the rat population, which has always found a ready meal in residents’ trash.

Early evidence shows that the plan is working: the number of rodent-related complaint and assistance calls to the city is down over the past few months, Cicilline said.

“Now on trash day, curbs in every neighborhood of our city are lined with what I consider our single most important tool in reducing the rodent population and creating cleaner neighborhoods — big green cans,” Cicilline said.

The cans were bought with $3 million set aside in the 2006 and 2007 city budgets. The distribution of the cans began last year when 15,000 were dropped off at a smattering of homes in Olneyville and South Providence in a pilot program. This year, the city tried to deliver about 600 cans per day to get them all passed out by the end of this month.

The city also expects that by introducing some rules with the cans and an understanding of human nature, the cans will have the effect of increasing recycling as well.

Until now, the city has been picking up however much trash a resident put on the sidewalk. Now, city collectors will pick up only the trash that is in the big can — essentially, imposing a 95-gallon limit.

“The city’s had a culture where we pick up whatever’s out there,” Ramirez said, adding that “95 gallons is more than sufficient” for the average household’s trash.

But it is probably not enough for its trash and recyclables, which can be bulky. A household should be able to dispose of all its trash if it puts recyclables into the recycling bins and trash into the big green can.

“If you don’t recycle, that can’s not going to be big enough,” Ramirez said.

By introducing the 95-gallon trash limit, John Nickelson, director of Public Works, hopes that the cans will help Providence save money in the long term by reducing the amount of trash the city generates, thus reducing fees to dump it at the state landfill.

“We’re going to evolve from the culture we’ve had. We know this is just the first step,” Ramirez said.

Cicilline said that the reception across the city has been almost entirely positive.

“I think everybody really loved getting their big green can,” he said.

But some residents found the 95-gallon cans too large to maneuver, prompting city officials to procure some 65-gallon bins as an alternative. The larger bins proved to be difficult for some elderly residents and those who have limited space at their homes or apartments.

Ramirez said that the city swapped some bins for the smaller models in late spring. “People who really had an issue would call in,” Ramirez said.

The smaller bins are available if residents call the Public Works Department.