The Frenchman previously stated that he would make a decision with regards to signing a new contract once this season finishes, suggesting that his time at the Gunners could be coming to an end.
"I would love to be here forever because that would make me immortal!" Wenger said in a news conference. "I love this club of course. I always said that our job is like you work like you are here forever and know that it can end every day.
"I'm very honoured to have the support of Stan Kroenke. That is something that is very positive for me. I've had consistent support from inside the club. I'm very grateful to this club because during my 17 years we have had ups and downs. They have always shown faith in me.
"We have a team now that can compete and that's what we want to show. I've turned many offers down [over the years]. I've always thought this club is special."
Arsenal are currently at the top of the Premier League table after five games.