Since the club announced Nuno Espirito Santo was set to depart, Portuguese compatriot Lage has been the firm favourite to take over at Molineux.
Eventually that appointment was made and Coady, who is away with England preparing for the upcoming Euros, says he is excited to work under the former Benfica boss.
“I think it’s always a little bit of a shock when your manager goes. It was a shock when we got told on the Friday,” Coady told talkSPORT.
“But the club’s moving forward and we’ve seen a new manager come in which is incredibly exciting for the football club, it’s incredibly exciting for us all. We’re all looking forward to working under him.
“I spoke to the club a few times which has been brilliant. It’s a really exciting time for the football club, we’re all excited because we all want to improve and get better.”
England get their tournament underway on Sunday when they face Croatia and Coady could be set to feature with fellow defender Harry Maguire battling for fitness.
The Manchester United man was absent from training on Wednesday and Coady insists the national team defenders are all ready if called upon.
He added: “He (Maguire) is a massive part of this team, he’s an incredible footballer and brilliant person so is fantastic to have around the camp. We know he’s got that experience of big tournaments and captaining Manchester United.
“We’re ready for whatever, we’ve not worked on anything in particular at the minute, we’re ready for whatever the manager wants.
“This team is full of world class players who play different ways for their clubs, different ways we try and bring together every single camp we have and it’s no different now.
“Whatever way the manager wants to move forward is great by us because we know we’re here to improve and to try and win as many games as possible.”