The Harry Potter author, who lives in Edinburgh, has also spoken out about her views in a blog post, stating that independence "carries serious risks".
Her donation was received by the pro-union campaign "recently", Better Together said.
Writing on her website, Rowling said that, while she is "no fan of the current Westminster Government", she has concerns about the economic risks of independence.
"My hesitance at embracing independence has nothing to do with lack of belief in Scotland's remarkable people or its achievements," she wrote.
"The simple truth is that Scotland is subject to the same 21st century pressures as the rest of the world.
"It must compete in the same global markets, defend itself from the same threats and navigate what still feels like a fragile economic recovery.
"The more I listen to the Yes campaign, the more I worry about its minimisation and even denial of risks."
She continued: "The more I have read from a variety of independent and unbiased sources, the more I have come to the conclusion that, while independence might give us opportunities - any change brings opportunities - it also carries serious risks."
Referring to her donation to Better Together, she wrote: "I wanted to write this because I always prefer to explain in my own words why I am supporting a cause and it will be made public shortly that I've made a substantial donation to the Better Together campaign, which advocates keeping Scotland part of the United Kingdom."
The author, who was born in the West Country, but has lived in Scotland for 21 years, said there is a "fringe of nationalists who like to demonise anyone who is not blindly and unquestionably pro-independence".
"I suspect, notwithstanding the fact that I've lived in Scotland for 21 years and plan to remain here for the rest of my life, that they might judge me 'insufficiently Scottish' to have a valid view," she said.
Referring to characters from her Harry Potter books, she added: "When people try to make this debate about the purity of your lineage, things start getting a little Death Eaterish for my taste."
Ms Rowling said her fears for the economy under independence extended to Scottish medical research.
She previously donated £10 million to set up a clinic at Edinburgh University to research treatments for multiple sclerosis, the degenerative disease that killed her mother.
"Having put a large amount of money into multiple sclerosis research here, I was worried to see an open letter from all five of Scotland's medical schools expressing 'grave concerns' that independence could jeopardise what is currently Scotland's world-class performance in this area," she wrote.
Referring to Alex Salmond's ambitions to create a common research area with the rest of the UK, she added: "In this area, as in many others, I worry that Alex Salmond's ambition is outstripping his reach."
Ms Rowling who lives in Edinburgh, concluded: "If the majority of people in Scotland want independence I truly hope that it is a resounding success.
"Whatever the outcome of the referendum on September 18, it will be a historic moment for Scotland.
"I just hope with all my heart that we never have cause to look back and feel that we made a historically bad mistake."
Labour's shadow Scottish secretary Margaret Curran said: "This is a significant and welcome intervention from one of this country's most talented and successful women.
"Separation is failing to win support among women and more and more of us are saying No Thanks to Alex Salmond's plan.
"It doesn't take a wizard to work out that Alex Salmond's case for breaking up the UK simply isn't a risk worth taking. The best way to make sure that we can make our country fairer is by working together across the whole of the UK, not putting a barrier between us."
Ms Rowling's donation is by far the largest received by Better Together, while Yes Scotland has benefited from £2.5 million from Colin and Chris Weir, who won £161 million in the EuroMillions lottery in 2011.
Asked for his response to the author's gift, David Cameron's official spokesman said: "You have heard the Prime Minister on a number of occasions say that he encourages and welcomes support for the case for the United Kingdom staying together from across all quarters."
The spokesman was asked at a regular Westminster briefing whether Mr Cameron would condemn abusive comments about Rowling which have reportedly been posted on social media websites since her announcement.
He responded: "There is never any place for abusive behaviour in whatever sphere of life."
A spokesman for Yes Scotland said: 'While we may disagree with her views, we of course completely respect J K Rowling and her right to express her opinion on the referendum and donate to the No campaign.
"And while we do not agree with her choice, we can all agree with her strong point that if the majority of people in Scotland do vote Yes, then she truly hopes that it is a 'resounding success'."