The presenter said his position would be made "unsustainable" by the "future working relationship" between TalkSport and The Sun, which News Corp also owns.
Murray, a Liverpool FC supporter, ended his message with #JFT96, a reference to the 96 Hillsborough victims.
Continued anger persists over The Sun's coverage of the 1989 disaster.
In his post, Murray said he had "delivered all-time record ratings" for the station and had been "offered a new contract until 2019".
The 39-year-old, who left BBC Radio 5 live for TalkSport in 2013, said his last show on TalkSport would be on 2 September.
A TalkSport spokesperson said Murray had been "a fantastic asset" and it was "very sorry to lose him".
News Corp's Â£220m purchase of Wireless Group, the owner of Talksport radio, was announced last month.
Shortly afterwards the station dispensed with the services of footballer turned broadcaster Stan Collymore.
"After eight extremely successful years at TalkSport, the station has decided to withdraw its contract offer from May this year," he revealed on Twitter.
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Broadcaster Colin Murray has announced on Twitter he is to quit his morning radio show on TalkSport, following its parent company's buyout by News Corp.