Norman will also become Chairman of the football club, with immediate effect, moving from his current role of Chief Executive. The documentation was finalised yesterday following extensive discussions between both parties.
Norman said: "I would like to reassure supporters this is business as usual.
"There is no-one more disappointed than me that Paul has decided to leave, but this is business and we have to move on.
"The infrastructure of the club is much improved compared to when we took over and we also have League One status. Paul has done an excellent job as Chairman and we thank him - but now is the time to look to the future.
"It's also important to understand that financially, this will not affect the club going forward. I have already invested heavily in Port Vale and will continue to do so. The financial security of the club is not in jeopardy.
"I've had meetings with Micky Adams and will also sit down with club personnel to ensure that we plot the best course of action for this season and beyond.
"The support of our fans has been nothing short of magnificent and I'm certain that will continue."
As well as Paul leaving the club, Operations Director Mike Aspinall and Finance Director Robin Anderson have also left. W Investment Group, owned by Paul, will provide consultancy services to assist the smooth transition of business operations.
Said Paul Wildes: "This has been an incredibly difficult decision for me and my main regret is that I am leaving the job half-finished.
"It has been clear from my many conversations with Norman that we have conflicting ideas on how to take the club forward. This sometimes happens in business and because of this, I have decided to step down.
"I know there will be a level of disappointment amongst sections of the supporters but this is not a decision I have taken lightly.
"Port Vale is now in a far healthier position than when Norman and I took over and I hope that it continues to prosper under Norman's guidance.
"I'd like to thank Micky Adams, the staff at the club and the supporters for their unwavering support since I became Chairman."