The attacker, 23, originally joined the Magpies on loan in the 2014-15 season but was unable to help the club avoid relegation to League Two.
After his release by Aston Villa that summer the Irishman joined Notts on a permanent deal, signing a two-year contract.
However the Dubliner has found game time difficult to come by since the departure of former manager Ricardo Moniz, being used mostly in cup competitions this season with only two starts in League Two.
Burke made a total of 52 appearances for Notts, scoring five times including a wonder-strike against his former club in a Capital One Cup tie at Villa Park in August 2015.
He leaves with Notts County’s best wishes for the future.