Cove boss Paul Hartley has already brought in striker Leighton McIntosh from Wrexham and Livingstone now makes the switch to the Balmoral Stadium.
The 22-year-old left back, who has had loan spells at Morton and Clyde, has agreed a two-year deal ahead of the 2020/21 campaign.
Hartley told the club website: "Adam is a very talented player with good experience of playing at Premiership, Championship and League 1 level, which was a big attraction to us. Gordon (Young) knows him well from their time together at Fir Park, which will help Adam settle in quickly."
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