Prime Minister Stephen Harper is expected to announce the agreement during a joint news conference with Premier Jean Charest in Quebec City on Friday.
Quebec is seeking $2.2 billion in compensation for agreeing to a harmonized sales tax around 20 years ago.
During the spring election campaign, the Tories promised to reach a deal with Quebec by Sept. 15, but the deadline was later extended to the end of the month.
The agreement comes after a series of events that may have tarnished the Tories in the eyes of many Quebecers.
A poor showing by the Conservatives in the province in the May election was followed by several moves that had many people in the province wondering whether they were being punished for voting the wrong way.
There was the refusal to let the army help with disaster cleanup during massive spring floods, Harper's appointment of a unilingual Torontonian as his communications director and moves to re-brand the Foreign Affairs Department and the Canadian Forces with references to the British throne.
Still, the Tories committed to giving Quebec $2.2 billion in exchange for blending the federal and provincial sales taxes.
But the negotiations were delayed as the two sides worked out technical details.
One potential sticking point was whether Quebec could be compensated for harmonizing its provincial sales tax with the federal GST, while still collecting the tax itself.
Earlier this month, Industry Minister Christian Paradis said Quebec will be able to continue collecting its own sales tax as part of the accord.
One contentious question has involved the list of items to be taxed. For example, products like baby cribs and books are subject to the federal GST but not the provincial sales tax.
Quebec did not receive compensation when it first synched the taxes, but it began asking for funds after Ontario and British Columbia received federal support for implementing the HST.
British Columbia, however, must return the $1.6-billion transfer after voters killed the province's HST in an August referendum.
Ontario, which received $4.3 billion from Ottawa, moved to the HST at the same time as B.C., but the reaction there was much less visceral.