The trio will be to the forefront of the battle for two promotion places from the Championship after Rangers joined the Edinburgh sides in the second tier of Scottish football following their stroll to the League One title last season.
Robbie Neilson has replaced Gary Locke in the Hearts hotseat, while Hibs also have a new man at the helm in Alan Stubbs and McCoist is waiting to see how both sides adjust to life in the Championship.
He expects a sterner test after two successive promotions and has warned his players about the growing expectation of the Ibrox fans.
"The big talking point over the summer has been the addition to the Championship of ourselves, Hearts and Hibs,” said the Rangers manager.
"I've had a chat with the boys and we've had a good blether about what's expected of us this season and how we see the competition and the games.
"There's going to be a lot of focus on this season and there's a real anticipation. I can feel it, not just from the players but from the fans and the staff as well.
"All being well, we can have a good pre-season and we can look forward to a very competitive and healthy start to the league.
"Hearts and, to an even greater degree, Hibs will have changed squads from last year and the change of management at both clubs will have a massive influence on their playing pools.
"The one thing the two Edinburgh teams both are though are really big clubs. There's no doubt about that and we've enjoyed going there on numerous occasions.
"We've had some great tussles at Ibrox too and I don't see next season being any different. It's bizarre we are all in the second tier but that's where we are at the moment.
"That's the madness of Scottish football but it gives us an opportunity to pit our wits against two of the country's great clubs and we are looking forward to that."
Meanwhile, Sky Sports understands that former Hearts defender Marius Zaliukas - who left Leeds United this summer - is set to seal a move to Ibrox.
Rangers are currently in the Highlands on a pre-season training camp, where they will face Buckie Thistle and Brora Rangers.