McKenzie is a free agent after being released by Charlton at the end of last season and he has signed a deal to play at Sixfields until the end of the season.
McKenzie will team up with former Sky Blues Marcus Hall, Kevin Thornton and Liam Davis and the news pleased Northampton boss Ian Sampson who told his club's website: "I am pleased to have got Leon in.
"He is an experienced striker with a good goalscoring record playing at a higher level. We have been struggling for goals and Leon will come in to try and change that. We have been looking to add to the squad and Leon fits the bill.
"He has got an excellent CV and a good pedigree and he has a hunger to get back among the goals. "We have been talking for a few days and he has been training with us and I am pleased we have got things sorted out. He is a player I have been looking at for a while and the cup run has allowed us to bring him in."