The Google-owned online media service came to an agreement with rights agency Merlin following months of negotiations, the newspaper said, citing sources familiar with the matter.
Contacted by AFP, Merlin declined to comment on the report.
Record labels representing 95 percent of the music industry have already signed up to the new terms but Merlin, which represents more than 20,000 labels from 39 countries, had been holding out.
YouTube earlier this year threatened to block the videos of artists like Adele and the Arctic Monkeys on its free site if they did not sign up to the terms of the subscription service.
YouTube is the world's biggest online source of free streaming music and the site has around one billion users a month.