Johnston, who guided the club to ninth place in the Scottish Premiership last season, has decided to leave the club at the conclusion of 2014-15.
This comes two days after his namesake, Michael Johnston, announced he would be stepping down from his role as chairman of the club.
The East Ayrshire side currently occupy eighth place and are without a win in their last four Premiership games.
Manager Johnston believes the club needs a new outlook in all aspects to give the fans what they deserve.
"The club and our fans need a lift and with the incoming chairman it is a good time to freshen things up across the board and generate some positivity around the place," explained Johnston.
"For now there is still a job to be done here and I will give 100 per cent.
"I have confidence in the players we have at the club and we still have the ambition of finishing in the top six."
Next up for Kilmarnock is a trip to Hamilton Acamedmical, a side they haven't lost to yet this season, recording a 1-0 win at home in December and a 0-0 draw earlier in the campaign.
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