The 35-year-old former Leeds Rhinos fullback, who has been working as an assistant at the Bulls since 2010, takes over from Mick Potter, who has returned to his native Australia.
Cummins was recommended for the role by Potter, with the appointment making him the youngest head coach in Super League after Trent Robinson decided to leave Catalan Dragons for Sydney Roosters.
"We had no hesitation in taking Mick's recommendation to offer Francis the job and we are delighted he accepted," Bulls chairman Gerry Sutcliffe said.
The struggling Bulls went into administration earlier this summer but have been granted a probationary 12-month licence to remain in the Super League.
Both Potter and Cummins had been working for free since administrators made them redundant in July, with Potter declining the club's offer of a new deal so he could return to his homeland.