Smoliy was born on 1 January 1950 in the village of Avratyn, Volochysk Raion, Kamianets-Podilskyi Oblast.

In 1970, he graduated from the historical faculty of the Kamianets-Podilskyi State Pedagogic Institute.

In 1975 he defended his candidate thesis "Union of the right-bank Ukraine with Ukrainian lands within the Russian state" (Ukrainian: Возз'єднання Правобережної України з українськими землями у складі Російської держави) and in 1985 his doctorate thesis "Social consciousness of Ukrainian national movements participants (second half of the 17th-18th centuries)" (Ukrainian: Суспільна свідомість учасників народних рухів України (друга половина XVII–XVIII ст.)).

In 1995, he became a full member, an academician, of the National Academy of Sciences of Ukraine.

In 1997–1999, Smoliy served as a Vice-Prime Minister on humanitarian issues in the government of Valeriy Pustovoitenko.