The 20-year-old right-back was one of five players who put pen to paper on new Gunners contracts on Wednesday, with Jack Wilshere, Alex Oxlade-Chamberlain, Kieran Gibbs and Aaron Ramsey also signing new deals.
Jenkinson feels the fresh contract is a pledge of commitment from both himself and the club.
"Obviously I'm over the moon - really happy," he told Arsenal's official website.
"I see my future at this football club and I'm delighted they see things the same way.
"Signing the contract shows commitment from me, which Arsenal can always count on, but it's a big commitment from them as well.
"People here clearly have belief in me, and now I have to make sure I prove them right."
Only 18 months ago Jenkinson was playing for Charlton, then of League One, and the youngster is happy with how his career has developed.
"I'm obviously really pleased with my progress over the past 18 months," he said.
"Of course there have been some challenging times along the way, and I've had to work really hard, but I'm pleased with where I am now and I'm so happy with the new contract.
"Now I just need to take every day as it comes, working and training hard."
Jenkinson believes having five of their young British players commit can only be a good thing for Arsenal.
"A big thing has been made of the fact that we're all British boys, and obviously that's great," said Jenkinson. "The guys who signed at the same time as me are all excellent young players and close friends of mine.
"I'm delighted not just for myself but for everyone else - it's great for the club as a whole, as well as for the players. We want to be playing with the best and believe we can do that here."