It was confirmed on Friday that the Frenchman had agreed fresh terms at the Emirates Stadium, signing a deal that will keep him at the club until the end of the 2016-17 season.
Wenger had come into criticism from some sections of support after failing to deliver a trophy for nine years, but that drought was ended with a 3-2 extra-time win over Hull City in the FA Cup final earlier this month.
And Keswick believes Wenger's new deal, which will take the 64-year-old beyond 20 years' service to the club, allows the Premier League outfit to look forward with great enthusiasm.
"We are delighted that Arsene has renewed his contract for a further three years," he told the club's official website.
"He is a man of principle, who lives and breathes Arsenal.
"He has established Arsenal for its exciting playing style around the world, continues his commitment to young players and has the ability to bring top-class players to the club.
"I have no doubt we have an exciting future ahead of us with him leading the team."
Majority shareholder Stan Kroenke echoed those sentiments, and hopes FA Cup glory can spur the team onto further success.
"Sustained excellence is the hardest thing to achieve in sport and the fact Arsenal has competed at the top of the game in England and Europe throughout the time Arsene has been manager, is the ultimate testimony to his consistency of performance, talent and ambition," he said.
"We are delighted with the FA Cup success which has added to his already outstanding record. Under his guidance we look forward to adding more trophies in future seasons."
Arsenal have not won the top-flight title since 2004, when they remained unbeaten throughout the entire league campaign.
