Deputies voted by 63 in favor, with 15 abstentions and one against, in support of Tarand, who had been nominated for the post by President Lennart Meri.
Tarand, 54, will take over from Mart Laar, who lost a confidence vote in September.
Tarand, a compromise candidate who does not belong to any party, has seven days to submit a new government to Meri for approval.
Earlier this month, parliament rejected Meri's first choice, central bank governor Siim Kallas.
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