The 45-year-old, who played for the club during the 1996/97 campaign, replaces Trevor Croly as Rovers aim for a late push for a European place in the League of Ireland.
Fenlon has been without a job since leaving Hibs last November and is understood to have rebuffed advances from Linfield, Sligo Rovers and Drogheda United.
Rovers host another of his former clubs, Derry City, tomorrow evening.
Fenlon said: "I am delighted to be taking over. The team is in a good position, so we'll look to push on and build on that. We will work hard to start on a positive note."