The 25-year-old has spoken of his delight at joining in the Premier League club but told of extensive interest for his signature.
He told RTL: "I am very happy to join a big club in Arsenal, one of the biggest in Europe.
"There were several clubs interested, but Arsenal was at the top."
Ospina has been told he will start the season on the bench due to the presence of first-choice keeper Wojciech Szczesny but will get his chance if he impresses in training.
"He [Wenger] told me that it all depends on me, my performances in training and then he will take a decision.
"I will have to adapt myself as quickly as possible [to the Premier League]. We all know it is very competitive."