Allardyce penned a two-year deal over the weekend.
"I'm delighted that he's signed," Nolan told whufc.com. "He has deserved it and it puts everything to bed. It's about him now going away and drawing up what he wants for next season. If you want this club to move forward I don't think there is a better man to have at the helm.
"I've worked under him at Bolton and I know what he's about. Not just on the pitch but behind the scenes. It's fantastic news for him and his family and fantastic news for us lads. I just hope that we can get a few new faces that will help us kick on again next season.
"I've just enjoyed working with him and I have a great working relationship with him. I've been his skipper for more than eight years in total and I've just got that relationship where he gives me all the responsibility in the dressing room.
"I'm just delighted to be able to work with him in the next few years that he's here."