The appointment was expected after his previous club Queen of the South revealed on Monday he had agreed terms with the Ayrshire outfit to become their new boss.
Johnston will take his Palmerston assistant Sandy Clark with him to Rugby Park.
The 39-year-old - who spent five years at Killie during his playing career - replaces Kenny Shiels, who left the club by mutual agreement earlier this month.
A statement on the club's website read: "Kilmarnock Football Club is delighted to announce our new management team of Allan Johnston and Sandy Clark.
"The management, staff and players all wish Allan and Sandy the very best in their new positions and look forward to the forthcoming seasons."
Johnston emerged as one of the front runners to succeed Shiels after an impressive first season in management with Queens.
He led the Dumfries side to the Second Division title, as well as the Ramsden Cup - which included a victory over Rangers at Ibrox.