The Czech Republic international ended an 11-season stay at Chelsea in June and signed for their London rivals in a move to the Emirates Stadium.
Cech, 33, has helped Arsenal to the top of the table and broke David James' Premier League record for clean sheets in his side's 2-0 win over AFC Bournemouth on Monday.
"It was not an easy decision but I always wanted to go to a team which could win," Cech told The Mirror.
"If I didn’t believe that I was going to a team which could win then I don't know why I would come.
"I play football, not to only enjoy it and I love the challenge of playing and competing with the best players, but I want to have the chance to win games."
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Cech, who won four league titles with Chelsea and is now with an Arsenal side top on goal difference, feels Wenger's men have what it takes to win their first league title since 2003-04.
"I believe this team has the qualities to win games and hopefully we will manage to go all the way in the league," Cech said.
"It's a very difficult and long run but I believe this team has the capabilities of doing it.
“We are in a good position, we are in the mix of the teams who will play to win the title so we want to stay in that position for as long as possible and every time we have a chance to improve our position then we would love to do it."