Anatoly Franchuk, appointed in a 63-0 vote by the Crimean parliament, is the father-in-law of President Leonid Kuchma's only daughter. Kuchma often stays at his Black Sea dacha.
Franchuk's election is part of a bitter power struggle between the strategic Black Sea region's president, Yury Meshkov, and parliament.
The appointment further erodes Meshkov's hold on the region.
Franchuk was nominated by the parliament's chairman, Segei Tsekov, after the legislature voted to strip Meshkov of virtually all his powers in the past week.
"This proves everyone thinks the president is incapable of heading the government," deputy Natalya Krasnovskaya said.
On Wednesday, lawmakers in the Crimean capital, Simferopol, amended the region's constitution to permit them to appoint a new government and formally dismiss Meshkov's team of ministers.
A spokesman for Kuchma said Thursday that the Ukrainian government had not yet formally recognized Franchuk, since the Meshkov government is still in place.
Born in central Ukraine, Franchuk has played down popular pro-Russia separatist sentiments in the volatile region and put a high priority on the need for economic reform.
More than two-thirds of Crimea's 2.7 million residents are ethnic Russians.
In a brief acceptance speech, Franchuk, formerly Crimea's minister of state enterprises, avoided any reference to the power struggle and pledged to appoint a new team of ministers within a week.
Ukrainian leaders want separatist clauses in Crimea's constitution annulled. Kuchma and Ukraine's conservative-dominated parliament gave Crimea until Nov. 1 to obey its directives or face tough unspecified measures.
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