Wildes, supported his business partner Norman Smurthwaite, had a bid of £1.25 million bid approved by the club's administrators Begbies Traynor.
The deal, which has also been approved by the Football League, sees the Valiants come out of administration, eight months after entering in March.
Wildes, who was named as the preferred bidder last month after Keith Ryder's summer-long bid came to nothing, told the club website: "I would like to thank the Port Vale supporters, once again, for their ongoing patience and support.
"It has been a long process but we are delighted to have finally taken over the club and look forward to a long and successful association.
"As I have previously stated, our intention is to develop the club both on and off the field.
"On the pitch we're continuing to support manager Micky Adams and the squad as they push for promotion. Off the pitch we have made some key appointments to ensure the immediate and ongoing success of the club."
Wildes will become club chairman whilst Smurthwaite will be chief executive, with Mike Aspinall taking up the role of operations director.
Financial director Robin Anderson will take responsibility for finance and IT departments and the club is also planning to appoint a commercial director.