"The council of ministers has decided to grant the pilot, Colonel Hassan Merei al-Hamade, political asylum," Jordanian Information Minister Samih Maaytah told AFP.
Earlier, a government official had said the Russian MiG-21 made an emergency landing at a base in Mafraq near the border.
Syrian state television said the plane was near the border when contact was lost at 0734 GMT. Jordan said it crossed the frontier minutes later.
The opposition Syrian National Council said: "The plane took off at high speed and flew at low altitude from a military base between Daraa and Sweida in the south of the country... to avoid detection by radar."
"The pilot is from Deir Ezzor (in eastern Syria) and his family is known for its opposition" to Assad's regime, spokesman George Sabra added.
The Syrian defence ministry denounced Hamade.
"The pilot is considered a deserter and a traitor to his country, and to his military honour, and he will be sanctioned under military rules," said a ministry statement carried by state television.
"Relevant contacts have been made with the authorities in Jordan in order to recover the jet on which the traitor pilot made his getaway."
Washington welcomed the defection.
"This is how these things start," said State Department spokeswoman Victoria Nuland said.
"It is obviously a significant moment when a guy takes a $25 million plane and flies it to another country."
Tens of thousands of soldiers have defected since the revolt against Assad's rule erupted in March last year, with thousands joining the rebel Free Syrian Army, according to the Syrian Observatory for Human Rights.
The air force had previously been seen as a loyal arm of the regime, however. Assad's father Hafez headed the service before seizing power in 1970, and air force intelligence remains one of the most feared branches of the security services.
Diplomats, meanwhile, stepped up efforts to stem the bloodshed, with Arab states demanding that Russia stop arming Syria. The United States and Britain were reportedly working on a transition plan.
"Any assistance to violence must be ceased because when you supply military equipment, you help kill people. This must stop," Arab League deputy chief Ahmed Ben Hilli told the Interfax news agency.
He also called for the mandate of UN and Arab League envoy Kofi Annan to be revamped, and for Iran's inclusion in talks on ending the conflict.
UN chief Ban Ki-moon discussed Syria with Iranian President Mahmoud Ahmadinejad on Thursday on the sidelines of a conference in Rio de Janeiro, a spokesman said.
Both London and Washington meanwhile denied a reports in British newspaper The Guardian that they were working on an initiative for regime change based on Annan's UN-backed plan that calls for a "Syrian-led political transition."
-- 'No new offer' --
Reports said Britain and the United States have discussed offering Assad immunity from prosecution if he steps down as part of a political transition.
But Britain's Foreign Office said "no new offer" was on the table and at the State Department, Nuland also said there was "no truth" to the story.
Russian Foreign Minister Sergei Lavrov, whose government retains close ties with Damascus, said any peace plan that calls for Assad to leave power and go into exile would not work because he would not quit.
"I do not think Assad will be sitting down at the negotiating table," said Lavrov, pointing to the results of a widely criticised May 7 parliamentary election which he said showed a majority still backed the Syrian leader.
In the latest bloodshed, nearly 170 people, mainly civilians, were killed, the London-based Syrian Observatory for Human Rights said.
"It's the bloodiest day since the start of the ceasefire (on April 12) and one of the bloodiest since the start of the revolt against the Syrian regime," Observatory director Rami Abdel Rahman told AFP.
Among the hardest hit was the central region of Homs, where 31 civilians and a rebel fighter died, the Observatory told AFP.
The bombardment halted attempts by the International Committee of the Red Cross and the Syrian Red Crescent to evacuate trapped civilians, but the agencies vowed to try again on Friday.
Hundreds of people are believed to be trapped in the historic heart of Syria's third-largest city, unable to flee or find shelter because of the fighting, the Geneva-based agency said.
More than 15,000 people have been killed since the revolt against Syrian President Bashar al-Assad's regime began in March 2011, according to the Observatory.