The approval came in a vote Saturday and by a simple majority of those present in the 249-seat body.
Parliamentarian Mohammad Iqbal Safi from Kapisa province and others say more than 150 representatives were present.
He said the vote was by show of hands, with an overwhelming majority approving and less than a handful rejecting.
Serious opposition to the measure had not been expected. The strategic partnership will now go to the Afghan senate, where it is also expected to be approved early next week.
President Barack Obama and Afghan President Hamid Karzai signed the agreement in Kabul on May 1.
It governs the relationship between the two countries through 2024.
THIS IS A BREAKING NEWS UPDATE. Check back soon for further information. AP's earlier story is below.
KABUL, Afghanistan - French President Francois Hollande for the first time provided details of his plan to pull France's combat troops out of Afghanistan by the end of the year, saying Friday he would leave around 1,400 soldiers behind to help with training and logistics.
The new French leader, making good on one of the major foreign-policy promises of his campaign, confirmed in a one-day visit to Afghanistan that all of France's 2,000 combat troops would be brought home by the end of this year putting France on a fast-track exit timetable that sparked consternation among some allies at a NATO summit in Chicago early this week.
Hollande's comments marked the first time that he had put an exact figure on the French deployment after the combat troops leave, suggesting that logistical necessities for France as well as its support for Afghanistan's hoped-for transition to peace will go well beyond the year-end target.
"The time for Afghan sovereignty has come," Hollande said during a meeting with French troops at a base in Kapisa province's Nijrab district. "The terrorist threat that targeted our territory, while it hasn't totally disappeared, is in part lessened."
Hollande, who took office last week, said that after more than a decade in Afghanistan, French combat troops had carried out their mission and it was time for them to leave in an early pullout coordinated with the United States and other allies. He said some trainers would remain to help Afghanistan's nascent security forces. NATO has set a pullout date of 2014, when Afghan troops are to take over security control.
The French leader met with troops and discussed plans with Afghan President Hamid Karzai to withdraw French combat troops two years faster than NATO's 2014 pullout schedule. Hollande's visit was not announced ahead of time for security reasons.
France now has 3,400 troops and 150 gendarmes in Afghanistan. Under Hollande's plan, some would stay behind to help send military equipment back to France, and others would help train the Afghan army and police. He did not provide a breakdown for the roles of the 1,400 soldiers who will remain past 2012 or how long they would stay.
"We won't have any more combat forces in Afghanistan after Dec. 31, 2012. I say specifically combat forces," Hollande said during a function at the French Embassy. "We will still have a military force that will be dedicated to the training of Afghan army officers that will also be present at the hospital, the airport and also will allow the Afghans to have a police force that is the most effective possible."
Hollande insisted France was not abandoning Afghanistan.
"This is a continuation, and there will be further engagement but in a different form," he said, such as in cultural and economic matters. "We want France to have a presence in Afghanistan differently from how it did in the past."
France has troops in the capital Kabul, in the Surobi district and Kapisa province to the east, and at Kandahar air base in the south where it has three fighter jets. A French military spokesman, Col. Thierry Burkhard, said most of the 2,000 who will leave will be those in Kapisa and Surobi. He said "hundreds" of trainers would remain, and soldiers conducting pullout logistics will leave bit by bit along with the withdrawing troops.
Hollande warned of possible problems in the pullout. "We will have to take every precaution. We must limit as much as possible our losses, make sure that there is no risk for our soldiers," he said.
Hollande said French equipment would be taken out by ground routes, but he did not say which ones. Pakistan closed overland supply routes to Afghanistan for NATO after a U.S. attack on the Pakistani side of the border killed 24 Pakistani soldiers last November. The decision has forced NATO to use a more costly route running through the north.
Reflecting increasing French disillusionment with the war, Hollande's conservative predecessor, Nicolas Sarkozy, had pledged to withdraw all troops by the end of 2013. Tension over Hollande's pledge to end France's combat mission a year earlier than that dominated the NATO summit, unleashing fears of a domino effect of other allies withdrawing early. France is one of the top troop contributors.
Hollande's campaign platform had first indicated that all French troops would be out of Afghanistan by then end of 2012, but in the late stages of the race he softened that to specify only combat troops. Guy Teissier, a lawmaker from Sarkozy's party who heads the defense commission of the National Assembly, pointed to a "contradiction" between Hollande's campaign rhetoric and his withdrawal plan after his election.
Teissier also said the quick pullout would expose French troops. "Once the combat troops are gone, who's going to protect the 1,000-odd soldiers responsible for bringing home the equipment we've left behind?" he said on BFM Television. "It's a very big risk for our soldiers ... It leads me to believe that Francois Hollande doesn't understand defense matters and world geopolitics."
"France gave its word to a commitment of the (NATO-led) coalition, and taking it back weakens it," he added.
President Barack Obama last year decided to pull out 33,000 U.S. combat troops by September. Gen. John Allen, the top U.S. and NATO commander in Afghanistan, said this week that on Sept. 30 there will be 68,000 U.S. and about 40,000 other coalition forces in Afghanistan compared to more than 130,000 last year.
The coalition has started handing over security control to Afghan army and police in areas home to 75 percent of the population, with a goal of putting them in the lead for all the country by mid-2013. NATO and other foreign forces would then be in a support role for the 352,000-strong Afghan National Security Forces.
Kapisa, where French forces are based, is one of the areas now being transferred to Afghan control. Ashraf Ghani, head of a commission overseeing the transition, said earlier this month that "the risks in Kapisa are containable and within our capability."
Keaten reported from Paris. Associated Press writers Mirwais Khan in Kandahar, and Angela Charlton and Sarah DiLorenzo in Paris, contributed to this report.