The Scot had previously remained silent on the issue, but posted a message on Twitter just hours ahead of the polls opening, to state his position.
He tweeted: “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!”
The Wimbledon champion has been quizzed on the issue previously but dodged the question, although in an interview in June he did criticise Scottish First Minister Alex Salmond for waving the country’s flag at the tournament last year.
Murray will not have a vote as he is not currently resident in Scotland, but he has generally been seen as a firm Scottish nationalist - drumming up controversy in 2006 when he said he would support “anyone but England” in the World Cup.
Last month he told the Guardian that he did not think it looked likely the result would be a Yes, but he added that his preference would be to represent Scotland if the country became independent.
“If Scotland became independent, then I imagine I would be playing for Scotland,” he told the newspaper.
“I haven’t thought that much about that yet because I don’t think it’s looking too likely that it’s going to happen. But if it did happen, then it would be pretty much the first time in my life that I would have ever (had the chance to play for Scotland).”
He added that he did not like making his views on politics known as previous comments had “caused me a headache ... and a lot of abuse”.