The 21-year-old was one of several players allowed to leave the former SPL side following their financial problems and subsequent exit from the league at the end of the season.
Osman has agreed a two-year contract with the Cobblers.
"I think he will prove to be another good addition to our squad," manager Stuart Gray said.
"We had him here training with us for a few days at the end of last season and that gave us a good chance to have a look at him.
"He is a good athlete, he is over 6ft tall and he is another young player who is very hungry for success."