The 24-year-old was released by Championship side Barnsley during the January transfer window and Cobblers boss Aidy Boothroyd has moved to sign the versatile defender, who can play at centre-back or left-back.
Collins began his career at Wolves before joining Port Vale on loan at the start of the 2008/09 season and then signing a permanent contract with the Valiants in January 2009.
His performances for Vale saw him join Barnsley on loan in March 2012, with a view to a permanent deal in the summer transfer window.
He moved on loan to Shrewsbury in the first half of this season before being deemed surplus to requirements at Oakwell.
Boothroyd said: "I like Lee and I think if you are going to be successful then you have got to get players in who are better than the level that you are at.
"Lee certainly is that and he played for us in a reserve-team friendly at Stoke in the week. He's been training with us and I am delighted we have been able to bring him in.
"He is a good defender, he can play in more than one position, he has a fantastic attitude and we had to fend off a number of clubs to sign him. I am delighted he is here."