The Polish goalkeeper made a number of fine saves to help the Gunners to a 1-0 win in the North London derby at the Emirates Stadium.
"He is over the problems he had last season," Wenger told the club's official website. "He had a dip in form, but has come back at the end of the season with good form and a good run, overall for me he is back to his best.
"We forget he is a boy who is only in his third season in the Premier League. He is only 23, for a goalkeeper that is very young. He was third then last season fourth in the Premier League, for such a young goalkeeper, that is not a bad achievement.
"I am sure you will see a great season from Szczesny, and I rate [Lukasz] Fabianski very highly, which is why I think we have two very good goalkeepers."
Szczesny has kept three clean sheets in his last four games for the club.