Ospina completed his switch to Emirates Stadium from Ligue 1 side Nice last month after impressing for Colombia at the World Cup.
The 25-year-old was drafted in as a replacement for Lukasz Fabianski, who departed for Swansea City upon the expiry of his Arsenal contract.
And Szczesny is more than ready for the fresh competition to be Arsene Wenger's first-choice keeper.
"I love a challenge," he told Arsenal's official website.
"I was expecting someone to come because Lukasz has left for Swansea and I wish him all the best. I knew someone would come in.
"I'm just going to do the same thing over again, I'm going to try my best in every game and every week in training. Hopefully that will be enough."
Arsenal have also added Alexis Sanchez, Mathieu Debuchy and Calum Chambers to their ranks in the close-season and Szczesny believes the club can mount a challenge for the Premier League title.
"We were close to being right near the top last year in the Premier League and we managed to win the FA Cup," he added.
"This year we added some players and we're looking stronger. The confidence is flying high and hopefully this year we can challenge for the Premier League."
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