Hayes had earlier confirmed his imminent departure following the end of his contract, while Celtic will not take up a one-year option on Simunovic's deal.
Celtic manager Neil Lennon said: "I would like to sincerely thank both Jozo and Jonny, brilliant lads who have given their all to Celtic over a number of years.
"Jozo has been part of our great club for some time and has given us some wonderful times, playing a really important part in our success. Jonny, too, has been an important player for the club in recent years.
"Above all, both are great men and everyone at Celtic wishes Jozo and Jonny and their families all the very best for the future. We are sure they will continue to be successful in everything they do.
"Both players leave Celtic as nine-in-a-row champions, something they have earned, an achievement they richly deserve and something I know they will cherish dearly."
Centre-back Simunovic made 125 appearances and scored five goals after joining Celtic from Dinamo Zagreb in 2015.
One of the 25-year-old's Celtic Park highlights was scoring the winner against Kilmarnock after 67 minutes while wearing the number five jersey made famous by Billy McNeill in the first game after the former Bhoys skipper and manager's death last year.
Simunovic has been managing a knee issue throughout most of his career at Parkhead.