The Spaniard was linked with a move to PSG earlier in the transfer window.
And Arteta revealed Bellerin has been a completely different player in training since they held an honest conversation about his future.
Speaking after Bellerin provided two assists in the win over Sheffield United, Arteta said: "Yes [I feared he may leave] because I understand that after such a long time at the club, and a lot of things that happened in that trajectory of his development, that he doubted whether he was still OK to continue here, what ambitions he had here, how he can evolve here.
"But what I liked is that he came to me and said, 'I can see what we are trying to do here and I'm convinced it's the right place for me'. Then when you close that window, you can open the next one. "He was a completely different player that I could see in training with his energy level as well, and his willingness to work a little bit more all of the time. We need to keep him fit as well, that's one of the issues he's had in the last few years because he's been really unlucky with injuries. You want to have that consistency and at this level of performance, you have to be fit. There's no other way."