Mirziyoyev, 58, was given the post after being backed by Senate leader Nigmatilla Yuldashev, who under the constitution should have become temporary leader ahead of elections.
The parliament also ordered a presidential vote, which many analysts expect Mirziyoyev to compete in and likely win, to take place within three months.
Uzbekistan strongman Karimov dies
Mirziyoyev was widely tipped by analysts to succeed autocrat Karimov after the 78-year-old was buried on Saturday in his native Samarkand city, of which Mirziyoyev was a former governor.
Mirziyoyev has had meetings with both Russian President Vladimir Putin who laid flowers at Karimov's grave on Tuesday, and Prime Minister Dmitry Medvedev, who attended the funeral.
Putin praised Karimov for maintaining "stability" over the course of his 27-year rule and said Russia would "do everything to support the Uzbek people and the Uzbek leadership."
"You can count on us fully, as you can on your most faithful friends," Putin told Mirziyoyev as the two met Tuesday.
Uzbekistan set to bury late strongman Karimov
Uzbekistan, a Central Asian country of over 30 million people, has one of the world's poorest records on human rights but has parlayed its strategic location on the border with Afghanistan into geopolitical influence.
The United States once maintained a military base there used for Afghanistan operations, but the government cancelled the lease after Washington called for an independent investigation into a brutal crackdown in 2005.
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