The striker left Southampton for Wolves in a £7.5m deal on deadline day. Armstrong has signed a contract to 2029 at Molineux.
Armstrong said: “I’m so proud and honoured to be able to represent this club. It was in the pipeline for a little bit, and it seemed to happen so quick.
"I’m delighted and over the moon – what a club to come to, with the history of the club, the fans, everything about it. Over the weekend things started to progress quite quick and before you know it I was travelling up here to get it all sorted.
“I’m honoured. I’ve played against the gaffer’s teams before and I know how he works. It’s such a hardworking, honest group, and I think you’ve seen that in recent games.
"I’m excited to become a part of the project and we’ll see what happens moving forward. All I can say to the fans is they're going to get 100 per cent from me every time I wear the shirt, which is the main thing.”
The Geordie also said: “Molineux is amazing. As an opposition player Molineux's a nice stadium, a good atmosphere, big pitch and they're only fond memories, but not for myself because we’ve always been beaten here, but I’m excited.”