You can do this with pretty much any semi professional painting program and a drawing tablet/display - procreate, photoshop, Krita, corel paintshop pro, etc. I looked through his website and couldn't find anywhere where he said what he used, and there isn't enough evidence to say one way or the other.
My favorite little known factoid is that when I googled his name Wikipedia says he's the guy who drew the pastafarian parody of The Creation of Adam, title "Touched by his noodly appendage".
From my time hanging out with Arne on IRC I would assume he's using Photoshop (or opencanvas version oc11b72 ;-) )... I'd be surprised if he's on a PS version newer than CS2 though. I think Adobe added a subscription model to later versions and back in the day (ca 2000) he was mostly just using regular round brushes. If that's still how he's working, I don't see any reason at all why he'd have upgraded. Perhaps he's written his own raster editor by now, though (another low-odds bet tbh).
You can read his art tutorial on his main page. But essentially, I think he strives to get a clean result (no scribbling to "find" the form) with as few brush strokes as possible, which takes a lot of practice. He's also does a lot of pencil drawing, obviously.
