The defender's previous contract was due to expire in the summer and injuries had restricted him to just six appearances this season.
Northampton boss Stuart Gray feels the 21-year-old has the potential to be an important player, but wants Johnson to prove his fitness.
"I think with Brett we could have a very good player on our hands because he can certainly play, but he has had a lot of injury problems in the last few months," Gray told the club's official website.
"If he can stay clear of injuries I think he will do well, but we need to sort his hamstring problems out, so we will be doing more investigative work into why he keeps getting the same hamstring injury.
"Fingers crossed he can get clear of those problems and then it will be up to Brett to try and impress me again at the start of next season.
"If he can get a sustained, injury free run then he will have the opportunity to show me what he can do."
Sky Sports