The England international, 26, completes the move to his hometown club on a three-year deal following a successful loan spell at St Mary’s last season.
He scored seven goals in 24 games and became the first-choice striker for new manager Ralph Hassenhuttl.
“It feels good,” Ings said. “Obviously, being here for a season already, I felt like it was very up and down for me personally, with a few niggles and small injuries, and that was off the back of not having a strong pre-season going into the season.
“Now I’ve signed permanently, I feel great. I’ve looked after myself over the summer and I’m just raring to go for the new season.
Wilfried Zaha always wanted to join Arsenal and has supported the club from a young age