The American singer-songwriter, who denied all of the claims against him, was alleged to have promised numerous women support in their careers before pursuing them for sexual relationships.
An email seen by The Independent to a fan who had purchased tickets to the tour via the company SeeTickets read: "The Ryan Adams UK & Ireland tour has been cancelled. Full refunds to ticket purchasers from authorised outlets will be processed by end of day on Monday. Please allow time for the repayment transaction to hit your account."
The Royal Albert Hall in London, where Adams was scheduled to play two shows this month, posted a similar message on Twitter.
Big Colors, Adams's forthcoming new album, was earlier pulled from its release schedule following the New York Times article.
Since the allegations were made, a number of musicians have spoken out against Adams's alleged behaviour.
Collaborator Jenny Lewis said she was "deeply troubled" by what she had heard and expressed solidarity with the alleged victims. Bridgers called on Adams's "network" of friends, bands and people he worked with to be held to account as well, while his former guitarist Todd Wisebacker condemned him and claimed everything he had been told was "a lie upon a lie".
In a statement via his lawyer, Adams said the accusations were "grousing by disgruntled individuals" who blamed him for "personal or professional disappointments".