"The latest toll we have is that 16 people are dead, as well as the two bombers," a police source said.
Police said one bomber had boarded each of the buses several moments before the explosions in the city centre.
"This attack was carried out by two suicide bombers who carried their charges for three minutes on the buses before blowing themselves up," one source said.
The explosions went off shortly before 3pm near the city hall, completely destroying one of the buses and setting ablaze the second which was just 100 metres away.
Text books and satchels, bought by parents on the eve of the new Israeli school year, were soaked in the pools of blood on the streets of the normally serene capital of Israel's Negev desert.
Police spokesman Gil Kleiman said no specific alerts had been received prior to the blasts but that there had been "general warnings".
Initial reports said there had been a third explosion in a nearby shopping centre but police said it was a false alarm.
The double blast was the deadliest since an attack on a restaurant in the port city of Haifa on October 4, 2003, which left 21 people and the female bomber dead.
The last Palestinian attack in Israel was on July 11, when a young woman soldier was killed in a blast at a bus stop just days after the International Court of Justice declared Israel's controversial West Bank barrier illegal.
Hamas said it had carried out the latest attack in response to the killing of two of its leaders in Gaza, Abdelaziz Rantissi and Sheikh Ahmed Yassin, in air strikes earlier this year.
"You are mistaken if you think that the assassination of our leaders will weaken our determination to continue our struggle," said a statement addressed to Sharon and Defence Minister Shaul Mofaz.
The premier said his government would not relax its "fight against terror".
"We have to fight terror - that is what my government is doing. The struggle against terror will be pursued to the fullest extent," he told reporters.
Public Security Minister Tzahi Hanegbi, speaking at the scene of the blast, said it appeared the attackers had managed to enter Israel from the southern West Bank, where the massive separation barrier has yet to be started.
"What we have learned in the last six months, since the attack at Ashdod (an attack in March that left 10 port workers dead), is that in places where the fence exists, there is no terror, and in places where there is no fence, there is terror."
Palestinian leader Yasser Arafat and his prime minister Ahmed Qorei both condemned the attack for targeting civilians.
"The Palestinian leadership has always maintained a clear position against any attack which targets Israeli or Palestinian civilians," a statement on the official Wafa news agency said.
"It is in our national interests that attacks against civilians stop so that Israel is not given a pretext to continue its aggressions against our people."
There was also widespread international condemnation of the bombings.
"Violence must stop," said EU foreign policy chief Javier Solana. "It seriously undermines all efforts to find a solution to the Middle East conflict."
In Washington, White House spokesman Scott McClellan said that "there is simply no justification for the killing of innocent civilians" while German Foreign Minister Joschka Fischer expressed "outrage" on a visit to Egypt.
Sharon had earlier unveiled an accelerated timetable for his controversial Gaza pullout plan, brushing aside opponents by predicting it would win parliamentary approval in early November.
A bullish Sharon told deputies from his right-wing Likud party that he would present the main legal provisions of his controversial project to pull troops and settlers out of Gaza to his security cabinet on September 14.
He will then present the full details to his cabinet on September 26, which is scheduled to vote on the project on October 24.
"I expect that on November 3, the law will be adopted in a first reading in parliament," he added.
The full legal provisions were not originally expected to be unveiled until early next year.