The Glasgow club is to make tampons and other sanitary products freely available in all women’s toilets at its home ground of Celtic Park by the time the next season starts in August.
The products will initially be provided on a trial basis.
However, the Scottish Premiership champions are expected to make the service permanent from December.
The announcement was made by Celtic fan Erin Slaven, a politics student at Glasgow Caledonian University, who started an online petition calling for the club to take action in March.
“Following discussions with the club around periods, period poverty and the visibility of female fans and our needs, we are delighted to announce that our club will lead the way as the first football club in the UK to provide free sanitary products,” she wrote on Twitter.
Ms Slaven said she had come up with the idea for the campaign while attending a Celtic match and mentioned it to her friends, who encouraged her to approach the club directly.
She added she would now like to see other Scottish football clubs, as well as others across the UK, follow Celtic’s lead and provide free sanitary products to their fans.
“We’re definitely hoping that Celtic will lead by example on this,” she said. “We’re aware that our club has got a great reputation. We’ve been champions for seven years, so with that reputation comes a responsibility to use that influence for the greater good.
“We’re hoping that other supporters will follow suit, but we’re happy to help in any way that we can. We’re talking about getting in touch with supporters’ liaison officers of other teams so we can expand it as wide as possible.”
Labour MSP Monica Lennon is poised to lodge a member’s bill at Holyrood putting a statutory duty on schools, colleges and universities to provide free sanitary products.
She described Celtic’s decision as a “brilliant victory” for the women who launched the campaign, adding she was delighted the club had taken such a “progressive step”.
“Menstruation should never be a barrier for women participating in football or supporting their team,” she said.
“As part of my ongoing campaign to tackle period poverty, I’m meeting the Scottish Football Association next month regarding its policies on menstruation for all football clubs in Scotland.
“Congratulations to Celtic and the campaigners who have fought for this positive step. I look forward to other football clubs and businesses across Scotland following their lead.”