"From my point of view his arrival is a massive relief because it would have been a nightmare to start the new season without a coach," McDonald said.
"Celtic fans want us to regain the title from Rangers but the first priority has to be to get the new manager on board with pre-season starting earlier than usual in July.
"Tony's an experienced coach so he will have his own ideas about how to take the club forward.
"I've never worked with him but everyone respects him as an attack-minded coach and his arrival gives the club the stability we need.
"It's a very exciting time for everyone connected with Celtic and I'm looking forward to being a part of the Mowbray era."
Rangers midfielder Kevin Thomson played under Mowbray at Hibernian and backed his appointment, but warned he has his work cut out for next season.
He told the Daily Record: "Celtic have got themselves the right man for the job. Tony is a fantastic manager.
"But let's not forget we have a fantastic manager of our own in Walter Smith and we are the team in the ascendancy now.
"I'm not going to say we are miles ahead of Celtic but I will say this, we are the champions and that means it's their turn to chase us.
"I think that's the hardest part of being at the Old Firm. Second best will not be tolerated but that's the situation Celtic find themselves in.
"We are in the driving seat right now and know the financial climate is a difficult one. That makes Celtic's task even tougher."