The vote followed a debate that stretched into the early hours of Wednesday morning.
A motion rejecting the financial framework around the so-called GTA Centre was defeated 7-6.
The proposed 20,000-seat arena is estimated to cost some $325 million.
Markham is a city of about 300,000 people just north of Toronto.
Councillors were expected to vote on the plan sometime late Tuesday night — but with at least 60 people or groups registered to speak on the motion, the final vote was pushed back to just before 3 a.m. Wednesday morning.
The big draw for many in Markham is the suggestion that the new rink could be a potential home for a new NHL franchise.
Dr. Ken Ng of the Chinese Chamber of Commerce called it a "once in a lifetime chance to leave a legacy."
Former NHLPA executive Paul Kelly said if the city doesn't act now it may miss the boat forever. "If you don't act now you'll likely never have another chance to get an NHL team," he said.
Under the proposal, half of the money would be put up by the Remington Group.
"It's unprecedented what Remington [Group] is doing, making this type of contribution towards an amazing facility for our city," said Markham Mayor Frank Scarpitti on Monday.
Although half the money would come from private sources, the other half would come from a levy on newly built homes, townhouses and condominiums.
"Based on the formula, getting half the money from Remington, based on the growth that's coming to the city of Markham over the next 20 years — that we know is coming — this is about as good as it gets anywhere in the country," Scarpitti told CBC News.
Toronto could support more than one NHL team, expert says
At least one expert thinks the GTA could support more than one NHL team.
Matthew Mendelson is the director of the Mowatt Centre at the School of Public Policy and Governance at the University of Toronto.
"The GTA is 10 times bigger than Winnipeg, it's 10 times bigger than Ottawa," he told Metro Morning, Wednesday. "The corporate concentration here, the wealth in this city compared to places like Winnipeg or Ottawa is astronomical."
Mendelson worked on a 2011 study that found Canada could support 12 NHL teams, including a second or third team in the GTA.
But while the study found the GTA could easily support a team, Mendelson said that doesn't mean it will happen anytime soon.
"The NHL is not a market, it's a cartel," he said. "It's controlled. They control their product and they determine where to put their teams based on other factors and those factors relate to their desire to build a market in the United States."
Arena plan faces opposition
The internal politics of the NHL aside, Markham's new area plan also has many detractors.
Many who spoke at the meeting said they don't want the arena paid for with public money. Coun. Don Hamilton said raising property taxes to pay for the project raises alarm bells.
"Members of the community that I've spoken to, they do not all support the city being financially involved [in the project]," Hamilton said.
Opponents also point to a lack of proven revenue sources for the arena if an NHL franchise doesn't materialize.
Marilyn Ginsburg of Grandview Residents Association put the vote in an historical context.
"The captain of the Titanic was waiting for info on conditions," said Ginsburg.
She warned councillors not to "wait too long or you'll go down with a sinking ship."