The Colombia international will officially become a Gunners player after their tour of the United States this summer, with a deal agreed to sign him from Nice.
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However, Wenger confirmed Szczesny remains the man in possession of the No.1 position, but fully expects the pair to vie for a starting berth.
"You know at the start Szczesny will be the No.1, then again we'll be down to performances and, if Ospina shows that he is better, he will play," the Frenchman told reporters.
Poland keeper Szczesny started all but one Premier League game last season, though Lukasz Fabianski - who has since left for Swansea City - was preferred in the FA Cup, which Arsenal won.
Ospina made 29 Ligue 1 appearances as Nice finished just two points above the relegation zone last term and impressed in Colombia's run to the quarterfinals at the World Cup in Brazil.