Ange Postecoglou is the toast of the green half of Glasgow after effectively sealing a 52nd Scottish title with Celtic.

The Bhoys' Australian manager was all smiles at Parkhead after watching his side come from behind to beat Hearts 4-1 on Saturday and — all but mathematically — secure the Premiership crown.

The victory puts Celtic nine points clear of sworn rivals Rangers, who have three games left but have a vastly inferior goal difference by 22.

The ecstatic scenes at Celtic Park were a testament to the remarkable influence former Socceroos boss Postecoglou has had since taking over a demoralised club in June last year.

Celtic had lost their way as Rangers — under their previous boss Steven Gerrard — ruled the Scottish roost but Postecoglou, originally received at Parkhead as "Ange who?" became a cult figure after rejuvenating their fortunes.

The 56-year-old restored the club's attacking identity while bringing in fresh ideas and personnel and his new-look Celtic now has its hand on its second trophy in his opening season following League Cup success in December.

It felt fitting that Celtic's victory on Saturday should come courtesy of goals from four of Postecoglou's inspired signings — Daizen Maeda, Kyogo Furuhashi, Matt O'Riley and Giorgos Giakoumakis.

Hearts had spoiled the party atmosphere early with a third-minute goal from Ellis Sims before Maeda and Furuhashi — both identified by Postecoglou during his successful spell in Japan — hit back before the break.

English-born Denmark Under-21 international O'Riley then fired in the decisive third after the break, before Greek international Giakoumakis sealed the deal in the final minute.

His latest success only enhances Postecoglou's standing as the most successful manager Australian soccer has ever produced.

He has coached title-winning teams in his homeland at South Melbourne and Brisbane Roar, in Japan with Yokohama F Marinos and now Scotland, as well as taking the Socceroos to the World Cup after guiding them to the Asian Cup title.

AAP/ABC