A government website reported on Thursday that 58-year-old Mirziyoyev was given the post by a joint session of both houses of parliament after he was backed by Senate leader Nigmatilla Yuldashev who “recused himself” from his right to take the post.
Under Uzbekistan's constitution, Yuldashev should have become temporary leader until an election is held later this year. The presidential election need to be held in the country within three months.
Analysts predict that Mirziyoyev, who has been the premier since late 2003, will be the winner in the presidential vote.
Karimov had ruled Uzbekistan since its independence from the Soviet Union on August 31, 1991.
He died of a stroke on September 2.
He was buried in his hometown of Samarkand on September 3. Delegations from 17 countries attended the funeral.