Arshavin has flown back to St Petersburg to sort out his work permit but hopes to be back in time for the North London derby at Spurs on Sunday.
He is not expected to play because he lacks match fitness, having had three months off since the end of the Russian season.
Manager Wenger said: “We are delighted to have signed Andrey. I’ve admired him for a long time.
“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.”
Arshavin added: “The Premier League is the top league in the world so I am so happy that I have this opportunity.”