"I might be on Friday or Saturday, but I'm not fit now," said the player. "It will be decided by Arsene whether I can play or not."
He will be unable to figure in the Gunners' Champions League campaign as he has already featured for Zenit in the competition.
Arsenal manager Arsene Wenger said: "He is a versatile player with great experience, who will add real quality to our squad.
"Andrey is an exciting impact player with a huge amount of ability and has been an influential force with both Zenit St Petersburg and the Russian national team in recent seasons."
The two clubs had earlier disagreed over the fee and over Arshavin's own personal terms.
But Arshavin flew to London on Sunday evening and spent Monday undergoing medical checks. It is understood he will now return to Russia to attend to personal matters before joining up with his new club.
Arshavin, who will wear the number 23 shirt for Arsenal, shot to prominence at Euro 2008 where his performances for Russia earned him a place in the Team of the Tournament.
He won the Russian Premier League with Zenit in 2007 and also played a key part in the club's Uefa Cup winning campaign last season.
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