The Harry Potter and Casual Vacancy writer was named as Robert Galbraith - the author of bestselling crime novel The Cuckoo's Calling - earlier this month.
Rowling had filed a lawsuit against Russells partner Chris Gossage and his friend Judith Callegari.
The High Court heard Russells had contacted Rowling's agent confirming that Gossage had shared the confidential information with Callegari, who had then told a journalist via a Twitter exchange.
The author was not in court today (July 31), but her solicitor Jenny Afia told Mr Justice Tugendhat that her client had been "left dismayed and distressed by such a fundamental betrayal of trust".
Rowling accepted damages from Russells - which she has donated to the Soldiers' Charity - and apologies from Gossage, Callegari and the company.
The law firm has also agreed to cover Rowling's legal costs.