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The 70-year-old's candidature was officially accepted by the Labour Party in Tel Aviv after she received 287 votes from her own central committee. Forty-five MPs abstained.
On Sunday she will formally succeed her political friend and colleague Levi Eshkol, who died of a heart attack last week.
Mrs Meir, who has come out of retirement to take up the role, pledged to maintain national unity and called on the people who worked with Mr Eshkol to "continue in the same framework" in her government.
She added: "I have never failed to accept party decisions and I shall not refuse now.
"I have faced difficult problems in the past but nothing like the one I'm faced with now in leading the country."
With her party controlling the largest faction in parliament, Acting Prime Minister Yigal Allon and Defence Minister Moshe Dayan have agreed to step aside and reserve their own bids for power until later in the year.
Following their decision, she was the only nominee put forward before the central committee.
Mrs Meir, a former schoolteacher in America, previously served as Israeli foreign minister for 10 years before she retired following ill health.
Because of her age and condition, her appointment is regarded by many as a stop-gap, intended to maintain national unity before the Labour Party chooses a leader for the October general elections.
Many supporters within the party consider General Dayan to be a more suitable candidate.
Acting Prime Minister Mr Allon also has substantial backing within the party leadership.
Both are younger than Mrs Meir and considered national heroes.
Despite such opposition, General Dayan, who is expected to retain his post as defence minister, said he would be honoured to work with Mrs Meir.
Her government is expected to reflect the same parties and ministers who previously served under Mr Eshkol.
Details of her new cabinet will be announced in the next few days.
Following her appointment Golda Meir won a convincing vote of confidence when she presented an identical cabinet to parliament to that of her predecessor.
Although many critics thought she would act as a stop gap, Mrs Meir went on to win Israel's general election in October 1969.
The Israeli prime minister governed using coalitions and to remain in office she had to ensure that she was publicly seen to support General Dayan despite the fact they were often at odds with each other.
For the next four years she remained in control but she was blamed for being caught off guard when war broke out between Israeli and Arab forces in 1973.
The Arabs eventually buckled under a sustained Israeli counter-attack but her reputation never recovered.
Mrs Meir won the general election in 1973 but continued to face stiff criticism.
As a result she resigned in April 1974.
She died four years later.
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