Broony says Celtic's main challengers will be Aberdeen and Hearts.
Celtic are gearing up for their first season under new manager Brendan Rodgers as the Northern Irishman looks to build on the foundations laid by former boss Ronny Deila - who won two Premiership crowns, before being dismissed - and lead the Glasgow giants to yet another league success.
Four of their five consecutive titles came after Rangers left Scotland's top flight, but their bitter Glasgow rivals are back next season - and will bring plenty of good players with them.
The Ibrox club have been busy this summer, recruiting a number of big names from down South in a statement of intent which has prompted suggestions whether they could even win the title on their return to the big time.
Hearts and Aberdeen were Celtic's closest competitors last season, although Deila's men won it comfortably in the end following a patchy few weeks, but Brown expects those two to boast the most threat to him and his team-mates again.
Celtic's Scott Brown misses his penalty during the shootout
“I think Hearts and Aberdeen have done great in the last couple of seasons,” he said via The Evening Express.
“They have challenged us all the way, and I think they are going to do the same."