The app, which debuted in 11 Western European markets in July, and then expanded to Australia last month, enables users to access an extensive on-demand archive of contemporary and classic BBC content.
Viewers in Finland, Sweden and Denmark can subscribe to the app for €6.99 a month, or €64.99 for an annual subscription, allowing them to stream content over WiFi or download programming to watch offline. They can also sample a selection of free content before committing to a subscription.
Available shows include comedies such as Little Britain, A Bit Of Fry And Laurie and Absolutely Fabulous; dramas including Silent Witness and Spooks, as well as factual shows such as Horizon and The Hairy Bikers.
Around 100 hours of new content will be added to global iPlayer each month, including themed collections and music programming, such as live shows from Paul McCartney, Robbie Williams and Oasis.
"This unique video on-demand product combines the classic with the contemporary and allows subscribers [to access] 70 years of brilliant BBC programmes, wherever and whenever they want," said Jana Bennett, BBC Worldwide president of Worldwide Networks and Global iPlayer.
"We launched the global BBC iPlayer because we think there's an untapped market for the 'best of British' shows, both for Brits living abroad and for all those people we know have a love of great British television."
The global version of the BBC iPlayer app is currently in pilot phase, presumably before Worldwide embarks on the key US launch later in the year.
Matthew Littleford, the new general manager for Global iPlayer, said: "We're proud to be one of the first international broadcasters to give access to our shows in a perfectly packaged app. Reviews of the app have been overwhelmingly positive since its launch in 11 other Western European countries and in Australia earlier this year.
"The extension into Finland, Sweden and Denmark is an important step in our strategy of pursuing multiple platforms for our programmes and brands, taking British programmes to new digital audiences around the world in an innovative, creative and easily accessible format.
"During this pilot phase we have an exciting vision for what this service could become and will develop it based on feedback from within all markets."