He is the 11th Brazilian member of the Shakhtar squad, who have won the Ukrainian Premier League for the last four seasons.
Atletico accepted Shakhtar's offer last week but Bernard, who was reportedly being chased by Arsenal, Tottenham Hotspur and Porto, was hesitant about the move, according to Brazilian media.
He left for Ukraine earlier this week saying only that he wanted to look at the club's facilities.
Shakhtar said on their website (www.shakhtar.com) that Bernard had been allowed to chose his shirt number and opted for 10, considered the most prestigious by Brazilian players. He has signed a five-year contract.
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Bernard, who is only 164 centimetres tall, was twice axed from Atletico Mineiro's youth divisions because he was considered too lightweight.
In 2010, Bernard, full name Bernard Alicio Caldeira Duarte, was loaned to third-division Democrata where he scored 14 goals in 16 games before returning to Atletico Mineiro.
He has thrived since Cuca took over as coach of the Belo Horizonte side two years ago.
Bernard scored on his last appearance for Atletico Mineiro one week ago but, having already been booked, was sent off for taking his shirt off as he celebrated.
Shakhtar, who have qualified automatically for the Champions League group stage, are rebuilding their squad after selling Brazilian playmaker Willian to Anzhi Makhachkala in February and his compatriot Fernandinho to Manchester City last month.
The club also sold Armeniaa attacking midfielder Henrikh Mkhitaryan to Champions League runners-up Borussia Dortmund last month but signed Facundo Ferreyra from Argentina's Velez Sarsfield for 9 million euros.
(Reporting by Igor Nitsak, additional reporting by Brian Homewood; editing by Amlan Chakraborty)
