The process of sourcing a replacement for the Glasgow midfield is underway - an announcement of which will be made in due course.
Warriors head coach Hugh Campbell said: "Andy's contract was due to finish with us at the end of this season. He requested an early release to pursue his playing elsewhere so it's by mutual agreement that he's leaving the Warriors and we wish him all the very best."
Craig added: "I've enjoyed my playing time and made a lot of good friends at Glasgow and when this chance came to play for Leeds, I thought it'd be another good opportunity for me and I'm looking forward to starting with them."
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