The former skipper made a loan switch, with an option to buy, on Monday – bringing to an end his seven years at Molineux.
Due to that option, which is reportedly around £12million, Wolves will not be able to recall Coady at any time this season.
Everton can exercise their permanent option on Coady at any point in the next year, which prevents Wolves from any opportunity to recall him.
Although the deal does not include an obligation to buy Coady, it is expected that he will make a permanent switch at the end of the season providing that his loan spell goes well and there are no serious injuries that jeopardise the deal.
Coady will also not be able to play against Wolves this season, when they travel to Goodison Park on Boxing Day and then welcome Everton to Molineux on May 20 – the final home game of the season and penultimate weekend of the campaign.
All parties are expecting the permanent move to go through next summer as Wolves prepare for life without their former captain.
Ruben Neves took the armband against Leeds, having been Coady’s vice-captain for some time. He is expected to become the new club captain following Coady’s departure.
Wolves are yet to announce who the new vice-captain will be, but Max Kilman and Morgan Gibbs-White both took the armband in pre-season.
Head coach Bruno Lage also referred to both of them as leadership figures in the squad, when quizzed about it last week.
Chelsea legend and former Villa coach John Terry has heaped praise on Everton’s business when Coady was announced on Monday.
He said: “Top signing this. Conor Coady and James Tarkowski give so much experience and quality to this Everton team.”
Meanwhile, Villa defender Tyrone Mings, who has a close friendship with Coady, said via social media: “So happy for you brother.”
Coady may come head-to-head with Mings and Villa on Saturday, as Everton travel to Villa Park for the early kick-off.
Speaking in his Everton announcement interview and when asked about the possibility of featuring against Villa, Coady said: “Without a doubt. I’ll be training all week and making sure I’m ready.
“I’ll be making sure I’m prepared right and ready if called upon to help my club and team-mates, that’s all I care about now.
“It (the World Cup) is something every English player wants to be a part of it.
“But all I want to do at the minute is to be a part of Everton football club
“The only thought on my mind is trying to help this club and make it better.
“It’s a proud day for my family. I’ll give my all every single day I come in here.”