Thomson was offered the role as new manager of Raith Rovers earlier this month but couldn’t agree terms. He remains on the shortlist for the vacant position at Dundee.
Kelty said in a statement: “Manager, Kevin Thomson, and assistant manager, Kevin McDonald, have today tendered their resignations which have been accepted by the club board.
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“Over recent weeks it became apparent that Kevin’s aspirations lay away from Kelty Hearts Football Club.
“We would like to thank them both for their efforts whilst with the club. This resulted in our promotion to cinch League One, winning the league by 21 points and reaching the fifth round of the Scottish Cup for the first time in our history.
“We would like to wish Kevin Thomson and Kevin McDonald all the very best in their careers going forward.
“The club have begun the process of identifying a new management team, we will update further as the situation develops.”
Thomson had three separate spells at Easter Road after coming through the club’s youth academy. A boyhood supporter, he played from 2003 to 2007 in the first-team before leaving for Rangers in a £2 million deal. He would later return for the ill-fated 2013-14 campaign as Hibs were relegated from the top flight before coming back a third time in the 2016 January transfer window.