The 24-year-old arrives from Club Brugge in a deal widely reported to be worth around 34 million pounds after an outstanding campaign in Belgium. Tzolis finished last season with 22 goals and 29 assists in 52 appearances across all competitions, earning a reputation as one of Europe's most exciting attacking players.
The winger has been given Arsenal's number 17 shirt, previously worn by players including Emmanuel Petit, Nacho Monreal and Alexis Sanchez.
Tzolis said he has followed Arsenal closely for years and was impressed by the quality of Arteta's side when the two clubs met last season.
"I love to watch football. I know everything about the Premier League, I know everything about Arsenal," he said.
"I watched so many games this year and especially when we played against each other. It was 3-0 at our stadium. I can say it was the most difficult team to attack against that I've played so far."
The Greece international said his main ambition is to help Arsenal compete for silverware while establishing himself in the team.
"My targets are to win titles, of course. I think for everybody the target is there, as many as possible," he said.
"For me the most important thing is to settle well in the team, have a good feeling, play as much as possible and then the rest will come. I'm sure about that."
Tzolis also spoke of his excitement at beginning his Arsenal career in front of the club's supporters.
"I'm very proud to be part of this amazing team. I'm looking forward to meeting everybody on the pitch, at the stadium, and to score my first goal at the Emirates."
He becomes Arsenal's latest arrival of the summer, following the signings of defender Piero Hincapie and goalkeeper Illan Meslier, who joined on a free transfer after leaving Leeds United.