The former Derby trainee, 19, has been on trial with the Grecians over the last few weeks, twice featuring for the club`s reserves.
Keane has been playing for Blue Square Bet North high-flyers Alfreton Town since leaving Derby last summer.
Exeter director of football Steve Perryman told the club`s official website: "Kallum is a young player who has decided he wants to put himself in front of us until the end of the season and show us what he`s got.
"It`s a chance for him not only to keep fit but to impress us."
Source: PA
Source: PA