The role was made vacant following the departure of Eddie Mitchell and was offered to Mostyn by new owner Maxim Demin.
Mostyn, previously chairman between March 2007 until 2008, will combine his new role at Dean Court with commitments on the FA Council as he looks to help the club continue its recent progress.
"Maxim and I are delighted to announce the appointment of Jeff Mostyn as chairman of AFC Bournemouth and we are positive he will do a fantastic job in his new role," chief executive Neill Blake told the club's official website.
"Jeff has been a constant at Dean Court for many years and has acted as a wonderful ambassador in his role as vice-chairman.
"We had no hesitance in appointing Jeff to the role and we firmly believe he has the credentials to help us reach the next level, especially when representing the club in the community and media."
Mostyn added: "It is an immense honour to be offered the opportunity to become chairman at a club I hold so dearly.
"AFC Bournemouth has been a massive part of my life since 2006 and I hope to help Maxim and the board realise their ambition to take this club even further.
"I am positive that I can contribute to the club's current upward trajectory, so It is with huge pride that I accept the position."