Roofe is a product of the Albion academy system and has been named in their first-team squad on two occasions. However, the 19-year-old is yet to make his senior debut for the Premier League club.
"Kemar is someone I have known since he was an Under-8 player," said Northampton boss Aidy Boothroyd.
"He is direct and creative, he is exciting and he can play in any attacking position.
"He has a very good character and he will be another very good option for us to have. I am very grateful to West Brom for allowing us to borrow him."