Murray, who has no vote himself as he lives near London, had previously refused to be drawn one way or the other on whether he backed secession, but his previous remarks on the issue had suggested he supported the union.
"Huge day for Scotland today! no campaign negativity last few days totally swayed my view on it. excited to see the outcome. lets do this!" he wrote on his Twitter feed.
In June Murray said he disliked a stunt by nationalist leader Alex Salmond who waved the Scottish flag after his Wimbledon victory last year.
Salmond held up Scotland's blue and white flag, the Saltire, behind British Prime Minister David Cameron's head as the crowd celebrated Murray's historic Wimbledon victory in July 2013.
"I started competing for Great Britain when I was 11. A lot of people forget that," said Murray.
Murray has tried not to air any political views after being slated before the 2006 World Cup when he said he'd support anyone but England, a remark he has said many times since was not serious.
(Reporting by Michael Holden; Editing by Guy Faulconbridge and Will Waterman)
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