The Track football ground has become home to Belgrave Wanderers after Rangers sold their share in the Amalgamated Football Committee.
The sale includes the Victoria Avenue Track's pitch, other facilities and Go Kart circuit.
Rangers, who have moved their games to St Andrew's over the past few years, said they felt it was the right time to sell their half of the Track.
The clubs said the move would ensure each had facilities in place in future.
In a joint statement they said that the deal allowed both clubs to strengthen their individual identities for the long-term.
The Guernsey Amalgamated Football Committee will continue to run the Track.
All of the island's major fixtures were played at the Track before they were moved to Footes Lane a few years ago.