Last updated: May 18, 2015 15:46
The 22-year-old, who helped QOS to the Scottish Premiership play-offs this season, will join the club on a three-year deal in July.
Holt joined the Doonhamers in 2011 and made over 100 appearances for the club.
He becomes Dundee’s fifth summer signing after Alloa defender Daryll Meggatt, Aberdeen’s Nicky Low, and strikers Rory Loy and Kane Hemmings signed pre-contract agreements with the Dark Blues.
Iain Davidson, Jamie Reid, David Clarkson, Paul Heffernan and Kyle Benedictus have all been made surplus to requirements at Dens and told they can leave the club.
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