Mr Dishon, who took over from predecessor Norrie Innes last February, revealed his intentions in his New Year message to the club fans.
He said he was standing down because other commitments did not allow him to devote the time and energy the role required.
He said: "I was delighted and honoured to take up the post of Chair of Clyde FC last February and I have thoroughly enjoyed my year in the post.
"It has been a tough year for me, both personally and with my day job, and the demands of this role is not one that can be underestimated.
"I have been considering my position for a while now and I have decided that I need to step down and allow someone else to take over that has the time and energy to commit everything to it.
"I am deeply saddened to be leaving Clyde. It is a wonderful club that I have genuinely fallen in love with."
The highlight of his time as chairman came in May when Danny Lennon's side ended the club's decade-long exile in Scottish football's lowest tier by winning promotion.
Mr Dishon said: I have the best of relationships with Danny and I would do anything to support him, as I genuinely believe there is no limit to where he can take us.
"We have a great base at Broadwood, a fantastic relationship with NLL and a dressing room full of talent, energy and passion, led by a brilliant management team.
"I will miss the trips on the team bus, I will miss going into the manager’s office after the match (win, lose or draw) and I will miss the good people at the club. Everyone has welcomed me - despite not growing up as a Clyde fan - but this Club will forever be in my heart and I will still attend matches when I can."
Mr Dishon said he will remain in the role while a new structure at the club, designed to ease the pressure on his successor, is introduced.
He said: "I will step down over the next few months once a few things are in place.
"The position of chair is currently split three ways, so we need to find three replacements to ensure the next candidate does not burn out.
"We need to find a finance director, to give the board a financial presence; a sporting director, to help Danny and Allan build a squad that is suitable and work within a budget and a new chair that can help to run the rest of the club.
"That is currently being delegated across the rest of the board, as well as keeping the links going with the Community Foundation - including the Schools of Football and Clyde FC Powerchair."