Both provinces proclaimed legislation allowing them to file a lawsuit on behalf of residents.
Manitoba filed its claim within hours after that, while Saskatchewan Justice Minister Gord Wyant said his province's claim would be issued soon.
Neither province indicated how much it is seeking in damages, but Wyant said Saskatchewan intends to hold the industry accountable.
"The health effects on Saskatchewan residents have been extraordinary over many, many years," he said in Regina.
"Those effects have cost our health-care system a tremendous amount of money and our intention is to move forward with this litigation against the industry to recover those costs."
Wyant said Saskatchewan will decide what those costs are through evidence that gets brought forward at trial.
In Winnipeg, Swan said treating diseases caused by smoking has been a big burden on health care.
"... what tobacco companies have done (is) to misrepresent their product, to hide the risks that were not known to people several decades ago, encouraged people to start smoking, allowed people to continue smoking," said Swan.
"And there's been an awful lot of loss, an awful lot of damage and an awful lot of suffering that's been inflicted on Manitobans by tobacco."
The Canadian Cancer Society said earlier this month that Manitoba has one of the highest smoking rates in Canada at 21 per cent for men and women.
The Manitoba government said in a news release that the defendants in the lawsuit include Rothmans, Benson and Hedges Inc., Philip Morris USA Inc., Philip Morris International Inc., JTI-Macdonald Corp., R.J. Reynolds Tobacco Company, R.J. Reynolds Tobacco International Inc., Imperial Tobacco Canada Ltd. and British American Tobacco P.L.C.
The tobacco companies have argued they are being unduly penalized by governments that regulate their behaviour and also share in the profits through tobacco taxes.
British Columbia, New Brunswick, Ontario and Newfoundland and Labrador have already filed similar lawsuits.
Alberta said Wednesday that it will also seek to recover $10 billion from tobacco companies to cover the estimated cost of caring for patients with smoking-related illnesses dating back to the 1950s.
Alberta is only the second province to put a dollar figure on its damages. Ontario is suing for $50 billion.
According to the Canadian Cancer Society's website, the Saskatchewan government expects to collect nearly $250 million dollars in provincial tobacco taxes this year. However, the society also said in a 2009 report that tobacco costs the Saskatchewan economy $1.1 billion annually, including $167.6 million in direct health-care costs.
— With files from Steve Lambert in Winnipeg