The Central Election Commission said Mirziyoyev scooped 88.6 per cent of the vote in yesterday's election, according to a preliminary count in this Central Asian country of 32 million which has no tradition of competitive elections.
Mirziyoyev's margin of victory to secure a five-year term echoes those won by predecessor Karimov, who died of a stroke in September after 27 years at the helm of the commodity-rich country.
An OSCE-led monitoring mission said there were "indications of ballot box stuffing and widespread proxy voting" during the vote.
Russian President Vladimir Putin "warmly congratulated" Mirziyoyev on his victory in a phone call and invited him to visit, the Kremlin said in a statement.
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Mirziyoyev, who was appointed prime minister in 2003, represents the same party as his former boss and even squared off against two of the pro-regime candidates Karimov had faced in the last presidential election in 2015.
Karimov's reign began in 1989 at the tail-end of the Soviet era and was often criticised for extreme abuses of human rights.
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