The 24-year-old, who joined from Barnsley in January, was a regular in the side that were only denied a place in League One in the play-off final.
Former Wolves trainee Collins becomes the second Cobbler to put pen to paper this week, following in the footsteps of captain Kelvin Langmead.
"I am thrilled that we have been able to retain Lee's services," manager Aidy Boothroyd told the club's official website.
"There has been a lot of interest in Lee and we had to fight off other clubs from a higher level for his signature.
"He is one you can rely on to help take us on to the next level and he is a player who could be playing higher than League Two."
Collins added: "The gaffer has shown a lot of faith in me and that means a lot. After the disappointment of Wembley there is some unfinished business here.
"I am buzzing to have signed this new contract and can't wait to get going again next season."