A British-Australian blogger and her Australian boyfriend were detained 10 weeks ago while travelling through Asia, The Times newspaper in London reported.
A British-Australian academic who studied at Cambridge University and was lecturing at an Australian university was detained separately and sentenced to ten years in prison, the newspaper reported.
The newspaper said she was being held in solitary confinement but it did not know what she had been convicted of doing. The lecturer has been behind bars for almost a year.
The three were being held in Tehran's Evin prison, where British Iranian Nazanin Zaghari-Ratcliffe, 41, has been detained since 2016 on spying charges, The Times said.
The women are thought to be the first British passport holders who do not also have Iranian nationality to have been imprisoned by Tehran in recent years.
Australia's department of foreign affairs and trade said it was providing consular assistance to the families of all three.
The department also urged Australians to follow its travel advice, which includes a warning that foreigners risk arbitrary detention in Iran.