Midfielder Medy Elito has agreed a move to another club after failing to confirm a new deal at Rodney Parade.
The quartet were offered new terms in May and Football League rules state that players must notify their club of their decision within a month.
Byrne has been linked with ex-County boss Justin Edinburgh's Gillingham.
Newport County have withdrawn contract offers to captain Mark Byrne, forward John Christophe-Ayina and Danny Holmes who will all now leave the club.