He accused his former master of carrying out "genocide" against his own people but said four decades of Assad family rule were collapsing.
"I announce my defection today from the regime of killing and terror, and I join the ranks of the revolt," Hijab said in statement read by his spokesman Mohammed al-Otri on Al-Jazeera news channel from Amman.
Otri said the defector was headed for Qatar.
Hijab's home province of Deir Ezzor in the northeast has been one of the key battlegrounds of the conflict and seen a mounting death toll from operations by the army.
The latest defection shows Assad has lost control of the country and that his people believe his days are numbered, a US official in Washington told AFP.
The surprise development was "just the latest indication that Assad has lost control of Syria and that the momentum is with the opposition forces and the Syrian people," National Security Council spokesman Tommy Vietor said.
The Syrian opposition in Jordan said Hijab and his family had slipped over the border during the night accompanied by two government ministers and three army officers.
"The Free Syrian Army helped all of them cross the border... Several other army officers defected and arrived in Jordan last night," said Syrian National Council member Khalid Zein al-Abedin.
-- 'Beginning of the end': SNC head --
SNC leader Abdel Basset Sayda said "this defection shows that the regime is disintegrating. It is the beginning of the end," while the Muslim Brotherhood hailed what it called "a courageous expression of great nationalism."
In Damascus, state television put out a terse report announcing that Hijab had been dismissed and replaced on an interim basis.
Information Minister Omran al-Zohbi later said defections at whatever level would have no impact on the Syrian state, while denying that any other ministers had switched allegiances.
The 46-year-old Hijab was only appointed on June 6 after a widely boycotted May 7 parliamentary election that was hailed as a centrepiece of reform by the Assad regime but dismissed as a farce by Arab and Western governments.
An agricultural engineer by training, he was agriculture minister under his predecessor Adel Safar.
Word of his defection came as the Syrian army readied a major ground assault against rebels in the northern city of Aleppo who say they control half of the city of some 2.7 million people.
It also came as a bomb blast rocked Syrian state television headquarters in the heart of Damascus, wounding several people just two days after the army said it had seized the last rebel-held area of the capital.
The morning bombing struck management offices on the third floor of the television building in the heavily protected Omayyad district of the city.
In Aleppo, the army bombarded a string of rebel neighbourhoods after government security officials said troops had completed their build-up and that a 20,000-strong force was poised for a ground assault.
A rebel commander was killed in the Salaheddin district in the southwest, and troops shelled the Palace of Justice as well as the Marjeh and Shaar districts, the Observatory said.
At least 21 civilians were killed in the city of Aleppo, said the Syrian Observatory for Human Rights, which gave a death toll of 137 across the country on Monday, including 82 civilians.
The head of the UN Supervision Mission in Syria, Lieutenant General Babacar Gaye, on Monday issued an appeal on behalf of civilians, amid fears of a looming bloodbath in Aleppo.
"I urge the parties to protect civilians and respect their obligations under international humanitarian law. Civilians must not be subjected to shelling and use of heavy weapons," he said.
A Syrian rebel group, meanwhile, which has claimed responsibility for the kidnapping of 48 Iranians in Damascus said three of its hostages were killed in shelling by government troops on Monday.