The Colombia international - who impressed at the World Cup in Brazil - completed his move from French side Nice on Sunday.
The goalkeeper is Wenger's third signing of the close-season and joins Alexis Sanchez and Mathieu Debuchy through the door at the Emirates Stadium.
With Arsenal ending their nine-year trophy drought last season with victory in the FA Cup, Ospina is confident he and his fellow new arrivals can bring further silverware to the club.
"I'm very confident. I believe we are putting together a brilliant squad, with top players," the 25-year-old told Arsenal's official website.
"Now we all have to be fit for the manager, and I'm confident things will go well, during games and training.
"[Alexis and Debuchy] are great players; they have both been doing very well at club and international level.
"It is great for Arsenal that players of this quality have joined the squad."
Ospina was a regular during his time in Ligue 1 where he made 189 appearances in the French top flight - having joined from Atletico Nacional in 2008.
He faces competition from last season's number one Wojciech Szczesny and Ospina is under no illusions as to the task he faces to play regularly in the Premier League.
"[Szczesny] is a great goalkeeper, very skilful. He has been a regular at a top side like Arsenal, so he is quality," the Colombian added.
"We also have the Argentine goalkeeper Damien Martinez. They are both young players but very experienced."