Ukraine's Deputy Prime Minister Oleksandr Vilkul said a successful bid would be a major boost for the country's tourism and sports industry.
"Forty-six million Ukrainians need more sports and tourism infrastructure in the Carpathian Mountains. Our athletes will be able to train at home and Ukrainians will be able to enjoy winter sports in our own country," said Vilkul, who also heads the bid committee.
The declaration signed by mayor Andriy Sadovyy and the head of the national Olympic committee Sergey Bubka comes just days before the November 14 deadline set by the International Olympic Committee for expressions of interest.
So far, only Kazakhstan's Almaty has officially confirmed its bid with Germany's Munich also intending to bid if a Sunday referendum is successful.
Earlier on Tuesday China's state media reported that Beijing and the northern city of Zhangjiakou will jointly bid for the Games. Other bids could also come from Poland and Norway.
Bubka, a former Olympic pole vault champion, said the decision to bid was proof of Ukraine's sports revival.
"Ten years ago I could not imagine that I would witness a Ukrainian bid to host the (Olympics). This confirms the revival of Ukrainian sporting traditions, the development of winter sports and a new focus on the Olympic values," he said.
Lviv, located in western Ukraine near the Polish border, hosted several matches during last year's Euro 2012 soccer tournament in Poland and Ukraine.
The Russian city of Sochi will host the 2014 Games starting in February.