The club could close temporarily and reopen after a massive refurbishment programme.
The building in Queens Gardens has been put up for sale and members are hoping a developer will seek planning permission to build flats on the site with a new revamped club underneath.
Members of the club, which has Eastbourne MP Nigel Waterson as its president, were summoned to an extraordinary general meeting on Friday night to discuss the plans.
A vote was taken and members voted in favour of selling the site and the redevelopment plans.
The club has been open for 120 years and is affiiated to the Association of Conservative Clubs. Over the years, countless Conservative MPS for Eastbourne have served as the club's presidents including murdered MP Ian Gow and Sir Charles Taylor. Edward Heath was also a member.
Conservative councillor Michael Tunwell is a lifelong member and was invited to step up to the role of president when Mr Gow was killed.
Club secretary Bryce Cooper said, "We have no intention of closing the club.
"The committee sought the approval of members for redevelopment plans and their approval means we can now move the whole project forward. It is a very positive thing.
"With building work going on, it could result in us having to close temporarily but the club will reopen in the new development."

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