They captured a series of strategic hilltops overlooking the town, where around 500 civilians are still living, according to the Britain-based monitor.
The advance comes as the UN refugee agency prepares to host a conference Wednesday in Geneva to secure concrete pledges from nations to resettle those displaced by the conflict.
IS had seized Al-Qaryatain in August 2015, kidnapping at least 230 people, including dozens of Christians, and razing the Mar Elian monastery.
The town lies on a key road linking Palmyra with the Qalamun region of Damascus province to the west.
Sunday's capture of Palmyra, known as the "Pearl of the Desert" for its colonnaded alleyways and stunning temples, was seen as the biggest blow so far in the war against IS in Syria.
- Regime hails Palmyra's fall -
Syria's government has described the victory as proof of its credentials in the anti-IS fight.
President Bashar al-Assad said the military advances would also help efforts to find a political solution by deterring countries that are "hindering the settlement".
In an interview with Russia's RIA Novosti state news agency, he named Saudi Arabia, Turkey, France and Britain as countries that are "counting on our defeat on the battlefield in order to impose their conditions at the negotiations".
"So these military actions and successes will lead to the acceleration of the political settlement, and not prevent it," Assad said.
Syria's armed forces have pledged to strengthen their hold on Palmyra and press on towards IS's northern bastion in Raqa as well as the oil-rich province of Deir Ezzor to the east.
France said the recapture of Palmyra was "positive news".
But the victory "should not exonerate the Damascus regime" of its responsibilities in the conflict, French Foreign Minister Jean-Marc Ayrault said during a visit to Algeria.
The jihadists swept into Palmyra, a UNESCO-listed World Heritage Site, in May 2015 and began a campaign to destroy tombs and shrines it considered idolatrous.
The extremist group demolished the 2,000-year-old temple of Bel and also blew up the Arch of Triumph.
- Deminers, sniffer dogs -
Syria's head of antiquities, Maamoun Abdulkarim, told AFP that 80 percent of the site was still "in good shape" and the ancient ruins could be restored in five years with UNESCO's help.
But UN expert Annie Sartre-Fauriat, who belongs to a panel on Syrian heritage set up by UNESCO in 2013, said she was "very doubtful" that would be possible.
As they retreated from Palmyra at the weekend, IS fighters planted roadside mines near some of the most celebrated ruins of the city.
Army sappers have already defused dozens of the makeshift bombs and have conducted controlled detonations of others, a military source told AFP.
On Tuesday, Moscow dispatched a group of Russian deminers, sniffer dogs, and advanced radar equipment to help secure the city, Russia's state media channel Pervy Kanal reported.
Moscow began its air war in support of Assad's troops on September 30, 2015, carrying out strikes on "terrorist" targets across the country.
The air campaign has been criticised by rebel groups, their Western backers, and rights groups as indiscriminate.
In the last quarter of 2015, Russian air strikes in Syria likely killed more than 1,000 civilians, the Airwars monitoring group said.
The London-based group gathered media reports, accounts from rebel groups and non-governmental organisations to compile the estimated toll.
It said its provisional view was that between September 30 and December 31, as many as 1,448 civilians were "likely" killed in Russian strikes.
Earlier this month, Russia announced a drawdown but it said it would keep up its support for the regime's battle against IS and other jihadist groups.
Analysts say only 10-25 percent of Russian forces have left Syria since President Vladimir Putin announced the withdrawal.
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