The world number 11 broke his silence on the subject with a tweet in the early hours of Thursday morning backing a ‘yes’ vote.
That left question marks over Murray’s continued commitment to the British team should the union remain in place.
The 27-year-old has always stressed his pride at representing Britain in Davis Cup and at the Olympics, citing the singles gold he won in London two years ago as of equal importance to his two grand slam titles.
And Murray told the Daily Mail: “I will be playing for Great Britain in the Davis Cup next year, that is for sure. I will be there in March. As far as I’m concerned the vote doesn’t change anything in that regard.”
Murray was earlier subjected to online abuse after declaring his support for the Yes campaign.
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!”
And he told the Daily Mail of his intervention: “I’ve followed pretty much everything about it over the last two weeks, and especially in the last few days, and that’s how I felt at the time
“It’s not my decision, I can’t vote, it’s for the Scottish people to decide and I trust them to make the right decision.
“I will support whatever the outcome is. Regardless of how it goes, I think it’s very important for everyone to come together and stick together afterwards.”
But his comments were met with abuse on the social media site.
Someone calling himself Harry S who tweets as @sportingharry wrote: “Wish u had been killed at Dunblane, you miserable anti-British hypocritical little git. Your life will be a misery from now on.”
Other users of the social media site were quick to condemn Harry S’s comments, with one tweeting: “you’re more of a disgrace to Britain than Murray ever will be” and another describing him as a “right horrible human being”.
Police said they are monitoring social media.
Assistant Chief Constable Bernard Higgins said: “People who put abuse such as this online should be utterly ashamed of themselves for making such vile, disgusting and distasteful comments.
“We are monitoring social media and where appropriate will take action against those involved.
“Social media is important for many people but it must be used responsibly. There is no place for personal abuse of any kind on it.”
Murray is the latest in a string of celebrities to be targeted online over their stance on the independence referendum.
Famous people who have urged Scots to stay in the UK - such as David Bowie and JK Rowling - have found themselves the subject of online abuse from pro-independence supporters.
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. In 2006, he courted controversy 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”.