"Arshavin is going to be the captain," the Dutchman, who is stepping down from his post after the EUROs to return to PSV Eindhoven, told reporters, according to the RIA Novosti news agency.
Arshavin has appeared rejuvenated in the last few months after rejoining his old club Zenit St. Petersburg on a loan deal from Arsenal in February, helping the Russian side to a league victory with a string of crucial goals.
His return to Zenit after a sometimes lacklustre three years at Arsenal was seen as ensuring his place in the national side, as Arshavin's scintillating performances at EURO 2008 was instrumental in helping Russia to the semi-finals.
Russia have been placed with co-hosts Poland, EURO 1996 finalists Czech Republic and the 2004 European champions Greece in EURO 2012 Group A.
Advocaat, who took Russian football by surprise by announcing he would not be extending his contract after the EUROs, suggested that Russia could even be an outside bet to take the title.
"When people talk about the EURO, they all talk about the Netherlands, Spain and Germany," he said. "But if we can play our kind of football as we are capable then we could be dark horse favourites."