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The Palmerston Park outfit confirmed the imminent departure of their boss, after he held talks with Killie chairman Michael Johnston.
Johnston - who spent five years at Rugby Park during his playing career - will replace Kenny Shiels, who left the club by mutual agreement earlier this month.
A Queen of the South statement read: "We can confirm that Allan Johnston has this afternoon agreed terms to join Kilmarnock FC as their new manager.
"The Board will meet this evening to discuss the position."
Johnston emerged as a leading candidate for the vacancy after an impressive first season in management with Queens.
He led the Dumfries side to the Irn-Bru Second Division title and the Ramsden Cup - which included a victory over Rangers at Ibrox.
Speaking last week, Michael Johnston said he was keen to make a swift appointment after receiving 40 applications for the job.
Praising the achievements of his namesake, the chairman said: "Allan's only been in management a year but has proved himself by winning the Second Division championship and also beating Rangers with Queen of the South at Ibrox.
"He's a former Kilmarnock player, still lives locally and knows the Scottish scene.
"He knows how to work with a tight budget and young players and he's ambitious.''
The departure of Shiels followed days of speculation about his future.
Killie finished ninth in the Clydesdale Bank Premier League but a four-match ban handed to the Northern Irishman following outspoken media comments -two of which were suspended - was also taken into consideration by the club.