The Under-19s Finnish defender completed a transfer from League One side Charlton Athletic on Wednesday for a fee thought to be in the region of £1m.
“It’s amazing to have joined,” the 19-year-old told Arsenal’s official website. “Words can’t really describe how it feels, to be honest.
“Being an Arsenal fan, it’s an amazing thing for me and something that I am really excited about. My dad has been a season ticket holder for 40-odd years and has been going regularly since he was a kid.
“He brought me up as an Arsenal fan and I've been going since I was young. I even went to a few games last season. My whole family are all massive Arsenal fans.”
Jenkinson expressed his gratitude to Charlton earlier in the week, saying that the club will “always have a place in [his] heart”.