After the operation on Sunday evening Hadassah hospital spokesman Ron Krumer said: "The operation was carried out with success and the prime minister has been immediately taken back to the neuro-surgical unit.
"The brain scan which was also carried out on Sunday showed no change," the spokesman said.
Earlier, the 77-year-old's chief surgeon said that the tracheotomy, which involves inserting a tube into a patient's windpipe, would help clean Mr Sharon's lungs and stressed it was not a sign that his condition was worsening.
"A tracheotomy is not a bad sign because it improves the cleaning of the lungs," Felix Umansky told news agency AFP.
"When we believe a patient is going to be intubated (fed and respirated by a tube) for longer than 10 days, it is convenient" to carry out a tracheotomy.
"There is no reason to be pessimistic. We are not giving Ariel Sharon enough time to recover, we must be patient. It is a long process."
Mr Sharon was rushed to hospital on January 4 after suffering a massive brain haemorrhage.
Cabinet meeting
Meanwhile, Israel’s interim leader Ehud Olmert and his vastly reduced cabinet made their first significant decision in the absence of Mr Sharon by voting to allow Arabs in East Jerusalem to vote in Palestinian elections on January 25.
The cabinet vote on East Jerusalem was approved by just seven ministers after four members of the right-wing Likud party pulled out of the governing coalition last week.
Mr Sharon’s withdrawal from the political scene threw Israel into political turmoil ahead of a general election scheduled for March 28.
Israel’s chief legal officer, Attorney General Menachem Mazuz, briefed Mr Olmert on the legal implications of Mr Sharon's continued incapacitation while paving the way for the appointment of a number of new cabinet ministers.
A senior government source said Mr Olmert, who currently holds a staggering 15 portfolios after a raft of resignations in recent weeks, would likely appoint three new cabinet ministers this week from his and Mr Sharon's new Kadima party.
"There will probably be three deputies from Kadima and the rest of the ministries will be shared out by other ministers" already in cabinet, the source told reporters on condition of anonymity.
He added that three former ministers from the centre-left Labor party who have joined ranks with Kadima would not be able to join the cabinet for legal reasons.
The trio includes former prime minister Shimon Peres who Sunday resigned his seat in the Knesset in a move that legal experts said would only allow him to re-enter government after the election.
The anonymous official also told reporters that Mr Mazuz, who has the power to declare Mr Sharon permanently incapacitated, would continue to classify him as temporarily out of action within a 100-day timeframe which would go beyond the March 28 election day.