Yatsenyuk, a prominent lawmaker, was a top figure in the protests against President Viktor Yanukovych, who fled the capital last weekend.
A group of interim leaders, including acting President Oleksandr Turchynov, also proposed other candidates for the new government to thousands of protesters who have set up camp in downtown Kiev. They were expected to be formally approved by parliament on Thursday.
Three months of protests forced Yanukovych to go into hiding over the weekend as his foes set up an interim government following violent clashes between protesters and police that left more than 80 people dead.
Russian President Vladimir Putin ordered military exercises to test the readiness of units in central and western Russia, Defense Minister Sergei Shoigu said in a televised statement. He said the exercise would "check the troops' readiness for action in crisis situations that threaten the nation's military security."
Shoigu didn't specifically mention the turmoil in Ukraine, which is bitterly divided between pro-European western regions and pro-Russian areas in the east and south.
In Ukraine's strategic Crimea region, fistfights broke out between pro- and anti-Russian demonstrators. About 20,000 Muslim Tatars who rallied in support of the interim government clashed with a smaller pro-Russian rally in the regional capital, Simferopol.
One health official said at least 20 people were injured, while the local health ministry said one person died from an apparent heart attack.
The protesters shouted and attacked each other with stones, bottles and punches, as police and leaders of both rallies struggled to keep the two groups apart.
They started to disperse after the speaker of the regional legislature announced it would postpone a crisis session, which many Tatars feared would have taken steps toward seceding from Ukraine.
"The threat of separatism has been eliminated," Refat Chubarov, the leader of the Tatar community in Crimea, told the crowd.
Crimean Tatars are a Turkic Muslim ethnic group who have lived in Crimea for centuries. They were brutally deported in 1944 by Soviet dictator Josef Stalin, but returned after Ukraine's independence.
The tensions in Crimea - a peninsula in southern Ukraine that is home to Russia's Black Sea Fleet - highlight the divisions that run through this country of 46 million, and underscore fears the country's mainly Russian-speaking east and south won't recognize the interim authorities' legitimacy.
Associated Press writers Maria Danilova in Kiev, Svetlana Fedas in Lviv, and Vladimir Isachenkov in Moscow contributed to this report.