He turned down Yanukovych's offer of the post of prime minister in January.
Tyahnybok has headed the nationalist, far-right opposition party Svoboda, or Freedom, for the past decade.
According to the biography on his party website, his early views were shaped by the surveillance under which the Soviet security service, the KGB, kept his family, and his grandfather's oppression under Stalin.
He studied medicine at college while also completing his military service. He got involved in politics while a student and joined the Svoboda party in 1991.
Tyahnybok was first elected to a local council position in 1994, aged 25, and was elected to the parliament four years later. He became head of the party in 2004, when it changed its name from the Social National Party of Ukraine to Svoboda.
Concerns have been raised in some quarters about the extremist views allegedly held by some members of the party.
But in an interview with the New York Times in 2012, Tyahnybok denied that Svoboda was anti-Semitic, xenophobic, anti-Russian or anti-European. "Svoboda is simply and only a pro-Ukrainian party. And that's it," he is quoted as saying.