The Spaniard, appointed on December 20, 2019 won the FA Cup in his first season before leading the Gunners back to the Champions League.
Arsenal, who have not won the Premier League since 2004 under Arsene Wenger, have re-established themselves as an elite club, finishing as runners-up to Manchester City over the past two seasons.
They are currently six points behind leaders Liverpool ahead of Saturday's match at Crystal Palace.
Arteta said he had enjoyed his time at the Emirates, where he also captained the team as a player.
"It's gone really fast and I'm really grateful to be in the position that I'm in right now, and that I have a lot to learn, a lot to improve and the best is yet to come," he said.
The 42-year-old said he was aiming for the "big trophies, without losing the rest of the things that we have built".
Arsenal have been drawn against Newcastle in the League Cup semi-finals and are third in the Champions League table after six matches.
Arteta, who said it was currently "impossible" to imagine managing another Premier League club, was asked at his pre-match press conference what had changed during his five years at the helm.
"From my point of view, the unity, the connection and the fact that we are competing on big fronts right now," he said. "We haven't managed to do that in the past few years. That's positive but there's still a lot to do."
"Looking back it's gone so, so fast," he added. "I enjoyed every minute of it when there were bumps in the road and when we had good moments and that's about it.
"I'm here because I'm so passionate about what I do and I love this football club and I want the best of that, so I just try to give my best version every single day."
"We've built something together and so many people have contributed in a big way to achieve that and the fact that everybody is hungry and ambitious," he said. "But now we have to go to another level."
