The state House and Senate voted today to override Governor Deval Patrick’s veto on an $800 million transportation finance bill, concluding months of argument and politicking to raise taxes that will pay for transportation maintenance and construction.

The bill — which raises the gas tax by 3 cents per gallon, adds a $1 per pack charge on cigarettes, and institutes a broad tax on computer software services — was passed by both legislative bodies last month, but became mired in controversy after Patrick voiced disapproval for the bill, arguing that it failed to address the uncertain future of tolls on the Massachusetts turnpike.

But Democratic legislators dismissed those concerns, saying that the current laws made it unlikely that tolls would end anytime soon. Today, they acknowledged that the bill was not perfect, but maintained that it was a significant step toward putting the state’s fiscally precarious transportation system on stable financial footing.

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The House voted 123-33 to override Patrick’s veto, with three Democrats and all Republicans voting to sustain the veto. The Senate voted 35-5 in agreement with the House, overturning Patrick’s veto.

The money the bill provides, which is estimated to ramp up to $800 million per year by 2018, will prevent the need for immediate MBTA fare hikes to close the T’s budget deficit, pay for the operation of regional bus services, fund Department of Transportation personnel costs, and finance some modest transportation projects.

Transportation advocates cheered the passage of the bill, though they maintained that there was more work to be done.

“We don’t see the passage of the transportation bill as a time to pause, but instead as a time to move ahead,” said Kristina Egan, executive director of the nonprofit Transportation for Massachusetts. “Now, we need to ensure that the new funding is spent fairly and wisely in every part of the state.”

After the vote, House minority leader Bradley H. Jones said he was disappointed with the outcome.

“In voting to sustain Governor Patrick’s veto, House Republicans were eager for the opportunity to get back to the transportation finance drawing board where we would have once again offered to the Legislature and taxpayers our transportation finance proposal – free of any statewide tax increases,” Jones said.

The hike on gas taxes will be enacted in gas stations around the state in one week.