Celtic CEO Kumbulani Konco a week ago denied reports that the club had recieved notification of the coach's resignation.
Jelusic's agent Ivica Stankovic also confirmed that no decision had been taken on his client's future at the time, as they waited for directives from the club amid their potential sale.
However, Stankovic has today told KickOff.com that an official notice of resignation has been tendered by the coach to the club.
"The coach has left Celtic. He has officially submitted his resignation," Stankovic says.
Jelusic arrived in South Africa just under a year ago after agreeing to a two-year deal with Phunya Sele Sele, and steered the club to an 11th-place finish in the Absa Premiership - just one point outside of the top-eight.
He also picked up the Coach of the Month award for October last year, after guiding the team to victories over reigning champions at the time Bidvest Wits, Cape Town City and Maritzburg United over the course of that month.