Johnston was until recently the club's only director but says he will now hand season-ticket holders as well as shareholders the chance to elect a new board member each.
Local politicians will also be invited to take part in the new company structure.
And Johnston has also revealed he has secured a £1million cash injection from local businessman Billy Bowie.
The Rugby Park chief has faced increasing pressure from the club's supporters following the controversial sacking of former manager Kenny Shiels in the summer, while his decision to offer Celtic fans discounted tickets for the sides' recent Scottish Premiership clash sparked fresh protests.
But he now hopes his latest concessions will win over supporters.
In a statement posted on the club's official website, he said: "I'm pleased to report that a further meeting took place yesterday at Rugby Park with Paul Goodwin of Supporters Direct.
"Billy Bowie and I reiterated to Paul our desire to promote community involvement in the new board of directors of the football club, which we intend to form following the implementation of our financial restructuring plan which we hope to conclude within the calendar year.
"Our shared vision is to have an open and transparent process for the election of a director by season-ticket holders and another director by shareholders holding under one thousand shares in the club. East Ayrshire Council would be invited to nominate a director and the Members of the Scottish and UK Parliaments representing Kilmarnock would be invited to join the board.
"We have invited Supporters Direct to investigate the creation of a working party which would embrace ALL supporters groups, along with local business leaders and politicians with a view to engaging in a constructive dialogue about the future of Kilmarnock Football Club and a careful consideration of good governance measures appropriate to our business model."
Bowie joined the Ayrshire club's board in August and has now confirmed his seven-figure investment - with Johnston voicing his hope it will persuade other local firms to do likewise.
"I'm delighted to report that Billy Bowie Special Projects Ltd has committed to investing a further £1million in the club to assist in the financial restructuring project which I have been working on for over a year with the full support of Lloyds Banking Group," said the chairman.
"Billy Bowie and I hope that this significant injection of capital will act as a catalyst for further investment by other local business leaders and result in a transformation of the club's balance sheet.
"Nothing on this scale has been seen at the club since the Moffat family invested around £4.3million over several years and Billy deserves our unqualified gratitude for his generosity. He is confident, as am I, that the club has a bright future if we all pull together."