Cozic told the club's official website: "I am pleased to have signed after a good season that was a learning curve for me.
"I enjoy playing in League One for Exeter and I am particularly looking forward to playing Plymouth Argyle."
The combative midfielder was involved on 33 occasions for the Grecians last term, scoring two goals for the Devon side.
The club have not disclosed details of the length of the new contract.
Source: BBC Sport
Source: BBC Sport