Bono was not in court to hear the verdict

Judge Matthew Deery at Dublin's Circuit Court ordered Lola Cashman to return the items, which also include earrings, within seven days.

He said he believed Bono's testimony that he had not given her the items which she tried to sell at auction.

After the verdict, Bono said they had brought the case out of principle.

Ms Cashman, who worked as U2's stylist in the 1980s, wrote an unauthorised book called Inside the Zoo, which upset the band.

When she attempted to put the memorabilia - which she said had been given as gifts - up for sale she was contacted by U2's lawyers.

She then began legal proceedings for defamation in London's High Court, which were put on hold for the Irish proceedings.

Bono said: "This case was brought very reluctantly, in the context of a larger dispute which we never invited.

"The point of principle involved was of much greater significance to us than any item of memorabilia."

Neither Ms Cashman nor any band members were in court to hear the decision.

Judge Deery said he found Ms Cashman's version of how she had been given the items at the end of a US tour doubtful, particularly her description of Bono running around in his underpants backstage.

Ms Cashman denied she stole the items

"It seems to me that Ms Cashman's version of events, the giving of the hat, is unlikely to have occurred," he said.

Bono had told the court he would not have given away the items, valued at �3,500, which he considered had iconic status, particularly the hat.

Judge Deery said he did not accept her claim that U2 had brought the case solely to stop the defamation proceedings, but recognised the outcome will substantially affect the other case.

"It would seem odd if the group were to make a provision to pursue a claim of this nature if the subject was not of importance to the band," he said.