"It was completed in extra-time but we must wait for confirmation (from the Premier League)," the Russia playmaker's representative Dennis Lachter was quoted as saying by the BBC.
Zenit general director Maxim Mitrofanov earlier told local Russian television the move could still be finalised after a spokesman for the club had said the deal was "definitely off".
"Both clubs definitely want to complete the transfer, therefore the negotiations are still going," Mitrofanov said.
Although the 27-year-old Arshavin was in London on Monday hoping to sign a contract, the clubs failed to announce an agreement before the 5pm transfer window deadline.
British media said terms had been agreed and the paperwork faxed to the Premier League with Arshavin agreeing a 3-½ year deal for a transfer fee of up to 15 million pounds ($21.35 million).
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