The 32-year-old Nigerian was a free agent after his release from Rotherham and he becomes Edwards' fourth summer signing.
Edwards told the club's official website: "I'm really pleased Kayode has agreed to sign for us.
"He's a powerful, aggressive striker who causes defenders lots of problems. He's good in the air, has a burst of speed and will give us some real strength in attack."
Last season the powerful striker scored eight goals in 33 appearances during his loan spell at Accrington and he has made over 500 professional appearances with eight different clubs since starting out with Bristol City in 1999.
Edwards added: "He'll bring our squad lots of experience which will be important to us next season."