The move had been awaiting confirmation from the Premier League after the clubs failed to announce an agreement before Monday's 5pm transfer window deadline.
"We are delighted to have signed Andrei Arshavin, he is a player I have admired for a long time," manager Arsene Wenger told the club's website.
"He is a versatile player with great experience, who will add real quality to our squad. Andrei 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 club said Arshavin, who won the UEFA Cup with Zenit last season and shone in Russia's run to the Euro 2008 semi-finals, had joined on a long-term contract for an undisclosed fee.
British media reported he had agreed a three-and-a-half-year contract and had cost Arsenal around 15 million pounds ($21.35 million).
NIFTY FOOTWORK
Television pictures showed a smiling Arshavin appearing in front of fans at the Emirates stadium holding a shirt with the number 23 and signing autographs.
"It was very hard days for me but now it doesn't matter, now I am a Gooner, it's important," Arshavin told Sky Sports News, showing that despite his nervous English he had already mastered some important Arsenal jargon.
He had been linked with several top clubs since lighting up last year's European championship in Austria and Switzerland with his nifty footwork and had even offered to take a pay cut to play abroad.
Arshavin, who holds a diploma in fashion design, usually plays the role of second striker but can also operate as an attacking midfielder.
Possessing creative flair and excellent ball control skills, he has been described by Russia coach Guus Hiddink as a player who "makes something out of nothing".
Arshavin could make his debut for fifth-placed Arsenal in the north London derby against Tottenham Hotspur on Sunday, although he cast doubt over his match fitness because the Russian season ended in November.
"I am not fit now. It will be decided by Arsene if I can play or not," Arshavin said.
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