The 25-year-old, who left Crawley Town at the end of last season, passed a medical with the Magpies on Tuesday before signing a long-term deal.
"Mustapha is a player I wanted to bring to Meadow Lane. I've seen him play, I've spoken to him and he has the right attitude, he wants to play for this club and he wants to do well here," Kiwomya told the club's official website.
"That's key for me, I need players here who want to be here, who want to succeed for this club, work for their teammates and for the fans who pay their money to come and watch them every week.
"Mustapha will add an extra dimension to our play, he is quick, he can play in a number of positions, he can be a threat down the wing but also a good defender, he should fit in well to the style of play that I will be looking to play this season."
Dumbuya, who is a Sierra Leone international, has also played for Doncaster Rovers.