The 25-year-old Polish international — who has signed with the Italian club for a season — looked likely to be frozen out for the upcoming campaign with Arsenal having signed Czech stopper Petr Cech from Chelsea.
The Gunners also have Colombian David Ospina, who replaced Szczesny as first choice in the Premier League matches last season, at their disposal.
“I believe he will have a future at Arsenal,” said Wenger.
“I rate him highly. I put him in the first team at the age of 20 and he already has huge experience.
“Roma is a big club, they play in the Champions League, play in a very different championship and that is a big experience for him.”
Szczesny, who only played 17 times in the Premier League last term but got rich consolation out of the FA Cup as he played in the 4-0 thrashing of Aston Villa in the final, conceded he hadn’t had the happiest of times last season but was ready to make the most of his opportunity at Roma.
“I had a difficult time last year – I’m the first person to admit that,” said Szczesny, who has played 180 times for Arsenal since joining their youth system in 2006 from Legia Warsaw.
“I didn’t have the best of seasons, that’s why things have turned out the way they have, but I’m grateful because it gives me the opportunity to join Roma this season.
“If I work hard – and with the help of the coaches – I’ll be able to help the team improve from last season and hopefully challenge for the title.” – Agence France-Presse