The 31-year-old featured in the Cobblers' recent pre-season friendly with Leicester before agreeing to a permanent stay at Sixfields.
Heath, who has also enjoyed spells with the Foxes as well as Coventry and Colchester, has played nearly 300 senior matches.
"Matty is going to help us out and he's very kindly agreed to join us on a non-contract basis," manager Aidy Boothroyd told the club's official website.
"He adds to our squad and he gives us a little bit more cover at centre-back. He has experience, he has height and power and he is a good organiser.
"I have worked with Matt before when I was at Colchester and I know what he will bring. He is a good professional, he will do a good job for us and I am pleased to welcome him in."
- Sports & Recreation
- Aidy Boothroyd