The Gunners confirmed on Friday that the Frenchman had signed a contract extension to May 2017.
Arsenal's transfer market activity - or perceived lack of it - has been a source of considerable frustration for some of their supporters in the last few years of Wenger's reign, which began in 1996 and saw its first trophy since 2005 when the north London outfit won the FA Cup earlier this month.
However, the 64-year-old has stressed the importance of having a "successful" time during the present transfer window as he looks to build on the cup triumph and deliver more silverware.
Asked about building another great Arsenal team, Wenger - a three-time Premier League winner and the division's longest-serving current manager - said on the club's official website: "It's time for another one.
"It's the start of a new team and I believe (the FA Cup) victory was crucial in that belief.
"We have shown signs the whole season that we can be a great side and now it's (important) of course to have another successful season.
"We know we have to... have a successful June and July, that's where you strengthen the team.
"It's very important that we are good now in the next two months until the end of August, that we can give to the team some more quality."
Asked about the fans expecting a big summer, Wenger said: "Yes, they should expect that.
"What I can promise is that we work very hard on a market that is very, very congested with many people who have a lot of money.
"But we have a big advantage, players want to join us and if we find the right quality I'm sure we can strengthen the team."
Wenger is optimistic that Financial Fair Play rules will work to Arsenal's advantage.
He said: "I believe (the club is in a strong position) because of the fact that we have built a stadium, the fact that we have paid a big part of the debt back and the weight of the debt back now is not as strong and heavy as it was before.
"The fact that the Financial Fair Play rule comes in hopefully will stop (the) craziness that happened in this (transfer) market.
"With these two (things) together, I think we can fight on a more even level than before."
This year's FA Cup was Wenger's eighth major trophy with Arsenal, with them having won that competition five times under him as well as the treble of league titles.
He has taken charge of 1,010 Gunners matches, reached the Champions League final in 2006, and is sure he and the club can "make some more history" together.
"I want to stay and to continue to develop the team and the club," he said.
"We are entering a very exciting period. We have a strong squad, financial stability and huge support around the world. We are all determined to bring more success to this club.
"The club has always shown faith in me and I'm very grateful for that. We have gone through fantastic periods and also periods where we have had to stick together.
"Every time when that togetherness was tested I got the right response. I think I have shown some loyalty as well towards this club and hopefully we can make some more history. I am sure we can."
A new deal for Wenger had been expected in the wake of the recent FA Cup final success over Hull, following a season in which Arsenal appeared ready to challenge for the league title before falling off dramatically in the second half of the campaign as injuries took their toll.
However, Wenger's side held off the challenge of Everton to qualify for the Champions League for a 17th consecutive season.
His prudence in the transfer market has served a purpose during the years when Arsenal have been paying for their move from Highbury to the Emirates Stadium in 2006, but it became a source of consternation as it continued after the board made it clear there was money to spend.
Wenger did splash out last summer, spending a club-record B£42.5million to sign Mesut Ozil from Real Madrid, but the midfielder struggled to maintain his early high standards as the team around him was decimated by serious injuries to the likes of Aaron Ramsey, Alex Oxlade-Chamberlain and Theo Walcott.
While many in the stands have wavered in their support for Arsenal's most successful ever manager, though, the board have remained steadfast.
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