Tzipi Livni became only the second woman in the Jewish state's history to be named foreign minister, while three other allies of Mr Sharon were brought into the cabinet.
The vacancies arose after four members of the right-wing Likud party, including Foreign Minister Silvan Shalom, resigned from the ruling coalition last week.
The new cabinet will only remain in place until a March 28 general election. It does not need the approval of parliament, which is in recess until the country goes to the polls.
"Our intention is to efficiently continue the work of government in all ministries," Mr Olmert said at a brief cabinet meeting.
Israeli cabinets usually feature around 20 ministers but the size has shrunk in recent months following the departure of the centre-left Labor and then Likud, leaving Mr Sharon's new Kadima party as the only one still in government.
Despite Mr Sharon's hospitalisation and the growing acceptance that he will never return to office, polls show that Kadima is still on course to emerge as the largest party at the general election.
Sharon comatose
Mr Sharon was placed in a coma as part of efforts to treat his brain haemorrhage but he has not yet regained consciousness.
A statement from Jerusalem's Hadassah hospital said the leader remained in a serious but stable condition after doctors successfully changed a respiratory tube overnight that had been inserted during a recent tracheotomy.
Mr Olmert told reporters on Tuesday of his intention to resume negotiations with Palestinian leader Mahmoud Abbas if he is confirmed as prime minister after March 28 and the Palestinians' own elections next Wednesday.
Mr Abbas, snubbed by Mr Sharon since June last year, responded by saying he wanted talks to resume immediately.
"The only way that we can forge peace is through negotiations and not through killings, assassinations, attacks and unilateral measures," he said.
Ms Livni launched her tenure at the foreign ministry with a withering attack on Mr Abbas's Palestinian Authority for allowing the radical Islamist movement Hamas -- responsible for the majority of attacks during the five-year uprising
-- to run in next week's parliamentary elections.
"Can you imagine any European country or the United States allowing a terrorist organisation to take part in elections?" she asked.
The build-up to the election has taken place against a security crisis in the Gaza Strip that has seen gunmen loyal to Mr Abbas's own Fatah faction take over offices of the central election commission.
But Mr Abbas insisted he had no fears about voters or the election organisers being intimidated on the day of the vote and said no one with weapons would be allowed anywhere near the polling booths.
"They will be conducted in a democratic and honest fashion and we will add to the Palestinian democracy that we have promised our people," Mr Abbas told reporters.
Settlers evicted
Meanwhile Mr Olmert ordered the army to evict dozens of Jewish hardliners occupying a Palestinian marketplace in the West Bank city of Hebron.
Following weekend riots, Israel security forces dragged supporters of the settlers out of the market on Tuesday, but dozens of others remain and the settlers themselves showed little sign of moving.
Authorities insist they are determined to remove nine Jewish families - around 50 people - squatting illegally in the market.
But hardliners have vowed to resist any evictions from what they regard as a sacred part of the land of Israel.
The market was closed 12 years ago after Baruch Goldstein, an extremist settler, shot dead 29 Palestinians praying in Hebron's Cave of the Patriarchs, a shrine holy to both Jews and Muslims.
Under a 1997 accord with the Palestinian Authority, Israeli troops evacuated 80 percent of the city, but continue to protect some 600 settlers living around the Cave of the Patriarchs.
In 2003, the Supreme Court backed an appeal by Palestinian traders ordering the settlers out and the market reopened, but it had was not implemented.