Sudan's Culture Minister Amin Hassan Omar and Jibril Ibrahim, a top rebel official, signed Tuesday's agreement.
Some Libyans mistrust Mr Jibril, since he served as Qaddafi's economy minister before turning belatedly against him.
And relations between Mr Jibril and Mr Tarhouni, a professor who used to teach in Seattle, have been scratchy.
But the dismissal of Jibril Rajoub, the head of the West Bank's Preventive Security Force (PSF), has proved much more controversial.
Jibril said the absence of a civic structure in Libya means people of all political ideologies can be part of a new government.
His deputy, Ali Tarhouni (pictured with Mr Abdel Jalil behind him), who holds the oil and finance portfolios, is set to replace Mr Jibril.
The idea was given tentative support by Britain's foreign secretary, William Hague who, with Mrs Clinton, had earlier met the Libyan opposition leader, Mahmoud Jibril.
He then spoke with Mustafa Abdel Jalil, Chairman of the National Transitional Council (NTC) of Libya, and Mahmoud Jibril, Head of the NTC Executive Committee.
Meanwhile Mahmoud Jibril, who has been the de facto prime minister in his role as head of the council's executive committee, stepped down on October 23rd.
On Sunday, Mahmoud Jibril outlined plans to put the various informal military units that have fought against Col Gaddafi under the control of the Transitional National Council.
And I want to thank President Jalil for his remarks and for all that he and Prime Minister Jibril have done to help Libya reach this moment.
PA's two powerful military chiefs, Jibril Rajoub and Muhammad Dahlan, who command the Preventive Security Force (the Palestinians are not allowed an army) in the West Bank and Gaza respectively.
In an interview with CNN's Christiane Amanpour last week, Jibril said that it is vital for Islamists, liberals and secularists to "sit around one table" and form a new government.
Since then, fighting between rebels and a Palestinian faction reportedly led by Ahmad Jibril, a longtime leader of the Popular Front for the Liberation of Palestine General Command, has rocked the camp.
But so far Mr Abdul Jalil and his de facto prime minister, Mahmoud Jibril, seem level-headed and sincere in their insistence that they want to help build a pluralistic and democratic state.
The NFA is led by Mahmoud Jibril, who was prime minister in the interim government that declared Libya a free nation after the 2011 revolt that toppled longtime ruler Moammar Gadhafi in October.
But it looked as if the party with the most votes was the one led by Mahmoud Jibril, a sensible modernising reformer who claims to be something between a secular liberal and a mild Islamist.
Among Mr Yusuf's many detractors, at least in private, are Muhammed Dahlan, the man with most of the responsibility for Gaza after the Israeli pull-out, and Jibril Rajoub, the head of the national security council.
ECONOMIST: Palestinian politics: No command and less control | The
Mr Jibril has promised that east, west "and even the cities still under siege, will be part of a new government", and the NTC says it could double in size to nearly 100 members once national liberation is achieved.
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