"Leon is a centre forward who gives us a physical presence, he is a proven goalscorer at this level, and we are delighted to get him into the football club ," said Stuart Gray.
"His goal ratio is very good, and hopefully he can reproduce that for us."
Constantine said: "I am happy to be here. It is nice to come somewhere where you are wanted.
"I have played here on numerous occasions and it is always been a good ground, it is a good club, and I am looking forward to playing here and looking forward to the challenge."