Yanukovych narrowly defeated Yulia Tymoshenko earlier this month, who aims to stay on as prime minister.
She had accused Yanukovych's Region Party of election fraud, but dropped a court case on the claims last Saturday.
But her refusal to step down as prime minister threatens to prolong the kind of political wrangling that has paralysed Ukraine's government for several years, deepening the financial crisis that shrank the economy by 15 per cent last year.
The parliament has not been able to pass a budget for this year.
Yanukovych enters office with a shaky mandate, inheriting an economy crippled by the global financial crisis and a nation whose political loyalties are deeply divided.
He has broad support in the Russian-speaking east of the country, but in the Ukrainian-speaking west, he lost in virtually every region to Tymoshenko.
His inauguration marked a comeback from humiliation five years ago when mass protests, called the Orange Revolution, overturned an election that had been rigged in his favour.