The 58-year-old, who led Ukraine to the 2006 World Cup quarter-finals in a previous stint, won a majority of the votes at a Ukraine Football Federation executive committee meeting.
"The head coach is always responsible for the result. I have a double responsibility taking into account the fact Ukraine co-host the Euro-2012 finals. We have to qualify from the group," Blokhin told a news conference.
Ukraine are co-hosting the tournament with Poland.
Kalitvintsev, who led the under-19 side to the European title in 2009 but failed to impress with the national team after taking over last August, will stay on as Blokhin's assistant.
Under Kalitvintsev, Ukraine managed a single 2-1 win against Chile but lost 2-0 to Brazil and Italy with other matches resulting in draws.
Former Dynamo Kiev and Soviet international striker Blokhin became the first Ukrainian player to win the coveted footballer of the year award in 1975.
FA president Hrigory Surkis last month mentioned three main candidates for the job - Blokhin, Kalitvintsev and under-21 coach Pavel Yakovenko.
Local media had reported Italy's former World Cup-winning coach Marcello Lippi was also a leading contender.
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