The highly-rated Tynecastle Academy supremo has left the Jambos after 14 years to join former skipper Steven Pressley who is the manager at the English League One club.
"The club has been particularly good to me during some difficult times with family illness," Murray told Hearts' official website.
"It's a big wrench to leave this football club and an even bigger wrench to, initially, leave my family up here. So it's not a decision that I took lightly.
"Going to Coventry City is a great opportunity for me and England is the next step in terms of my development, so it's exciting times.
"I'd like to thank Hearts and I'm going on good terms."
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