The date for all troops to leave Iraq will be December 31, 2011, he said.
These dates are "set and fixed" and are "not subject to the circumstances on the ground," he said.
Twenty-seven of the 40 Cabinet members in attendance voted in favor of the agreement, said Iraqi Foreign Minister Hoshyar Zebari. One minister abstained.
The Cabinet consists of the prime minister, two deputy prime ministers, and 37 other ministers.
The approved draft will be sent to the Council of Representatives, Iraq's 275-seat parliament, later Sunday, where it will be put to another vote. "There is great optimism that they will pass it," said Industry Minister Fawzi Hariri.
Al-Dabbagh said the parliament speaker and his deputies will decide when the parliament will vote on the agreement. He said there were "positive attitudes" when the major political blocs met to discuss the draft plan on Saturday.
Zebari said the parliament will reach a decision before it takes a 15-day recess on November 25.
"While the process is not yet complete, we remain hopeful and confident we'll soon have an agreement that serves both the people of Iraq and the United States well, and sends a signal to the region and the world that both our governments are committed to a stable, secure and democratic Iraq," said Gordon Johndroe.
"While there is still much work to be done, U.S. forces continue to return home and there will be 14 Brigade Combat Teams at the end of this year, down from 20 at the height of the surge," he added.
Earlier, Sami al-Askari, an adviser to the Iraqi prime minister, said the draft included changes that made it "satisfactory" for the Iraqis.
For months, the United States and Iraq have been negotiating a proposed status of forces agreement. It would set the terms for U.S. troops in Iraq after the U.N. mandate on their presence expires at the end of this year.
Many Iraqi officials say they will oppose any deal that hints at compromising the country's sovereignty.
Iraqi cleric Grand Ayatollah Ali al-Sistani said in a statement on his official Web site last week that he will "forbid any stance that targets the sovereignty of Iraq no matter how small it is."
In late October, Iraqi officials submitted several amendments to the draft plan to U.S. negotiators in Baghdad.
Zebari said at the time that the proposed changes called for a fixed timetable for U.S. troop withdrawal; a specific number of sites and locations that would be used by the U.S. military; and Iraqi jurisdiction over U.S. forces who commit certain crimes in Iraq.
Al-Dabbagh said the Cabinet on Sunday also approved a "draft framework" agreement between the U.S. and Iraq.
This agreement "establishes the principles of cooperation and friendship in the political, diplomatic, educational, health and environmental fields in addition to economic, energy, information technology, communication fields," al-Dabbagh said.