"Bakhit's mission is to take practical, quick and tangible steps to launch true political reforms, enhance Jordan's democratic drive and ensure safe and decent living for all Jordanians," a palace statement said.
The new prime minister said he is "committed" to reforms.
"We are committed to taking concrete steps to enhance political, economic and social reforms," he told AFP.
But Zaki Bani Rsheid, a leader of the Islamic Action Front (IAF), said Bakhit, who previously served as prime minister from 2005 to 2007, "is not a man of reforms."
"He carried out the worst parliamentary elections in Jordan in 2007. He is not the right person to run things at this current state and get Jordan out of crisis," Bani Rsheid told AFP.
The Islamists have long charged that the 2007 election was rigged after only six of the IAF's 22 candidates were victorious that year, a tally sharply down on the 17 seats the group won in the previous polls in 2003.
Loyalists of the king again won a landslide in new elections last November after the IAF boycotted the poll in protest at constituency boundaries they said under-represented their urban strongholds.
"We need a man who is well-respected by the people, a man who does not have a history of corruption and oppression. How can he (Bakhit) lead political reform?" Bani Rsheid asked.
Bakhit said he will give priority to "starting a dialogue with all segments of society."
"Dialogue will be inclusive to help build strong and capable political parties," he said, adding that the Islamist opposition "will be among the first to be included" in the process.
IAF chief Hamzah Mansur said that "with the choice of Bakhit, it's obvious that reforms have not started yet".
"We are against Bakhit because our experience with him is not encouraging," Mansur said.
"There is no reason to stop the protests now," he added, referring to his party's calls for a sit-in outside the prime minister's office.
Mohammad Masri, analyst and researcher at the University of Jordan's Centre for Strategic Studies, said selecting Bakhit was "strange."
"He was a source of tension in the local political sphere when he was prime minister, not to mention the worst elections in Jordan," Masri told AFP.
"People will find out if problems will remain or not after the composition of his government has been announced, and after they see and feel quick decisions on the ground, with tangible results."
The Islamists said on Monday that they had started a dialogue with the state and that, unlike the situation in Egypt, they were not seeking regime change.
They said they were demanding the resignation of the government, the amendment of the electoral law and the formation of a national salvation government headed by an elected prime minister.
Despite recent government measures to pump around 500 million dollars into the economy in a bid to help improve living conditions, protests have been held in Amman and other cities over the past three weeks to demand political and economic reform.
"Sacking the government was in line with people's demands," Masri said.
"But this could also mean that protests might continue until all demands are met. If the new prime minister does not move quickly, his government will be born dead."
Tunisia's popular revolt, which ousted veteran strongman Zine El Abidine Ben Ali, has inspired dissidents across the Arab world.
In Egypt, demonstrators have been protesting for eight straight days against President Hosni Mubarak, wanting him to step down after three decades in power.
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