The 34-year-old, who will captain the Swtizerland national team at the World Cup, has been assigned the No 12 shirt for the north London giants.
It is also claimed that if he can not agree a new deal with Manchester United, then Fellaini would favour a transfer to Arsenal over AC Milan, who are also said to be interested in the Belgian midfielder.
In a statement on his official Twitter page, Lichtsteiner said: "Happy and honoured to be a Gunner!".
"It's a great moment for me after Juventus to come to Arsenal, I have this big challenge to try to make big things with this big club", Lichtsteiner told Arsenal player.
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He leads Switzerland into his third World Cup next week.
He said: "It's hard to see a club like Arsenal not playing in the Champions League".
Lichtsteiner has already endeared himself to Gunners fans after being part of the Juve side that knocked out Spurs in the Champions League in March in the round of 16. "Stephan will improve us on and off the pitch". "The big objective is to come back on the highest level".
Lichtsteiner began his senior career at Swiss club Grasshoppers Zurich in 2001 and played for Lille in France, as well as Lazio in Italy before joining Juventus in 2011.
The 31-year-old was a key figure in the defensive setup of the Old Lady last season and helped them in securing their fourth successive domestic double - the Coppa Italia and Scudetto.