Microsoft's gaming arm said Xbox All Access will be introduced in the UK on November 5.
The scheme offers an Xbox console and membership of its online Game Pass Ultimate service, which gives access to more than 100 games, for a monthly charge paid over the course of two years.
The service was first tested in the United States in 2018, but will now receive a full launch for the first time in the UK, US and Australia.
Different versions of the programme will be available for each of the three current Xbox console models available.
Subscribers will also be able to choose to upgrade to the firm's next-generation console, currently known as Project Scarlett, when it is released at the end of next year.
Microsoft general manager of platform and devices marketing Jeff Gattis said the new service is a "first of its kind" programme.
"By design, the consumer is at the very centre of Xbox All Access. Xbox All Access gives players everything they need to start playing, on the latest devices with the latest games.
"Not only does the purchasing flexibility benefit the customer, but the content and quality of the programme does as well," he said.
"This is a first of its kind programme for Xbox, and we're pleased to be providing new ways for gamers to experience the best value and choice in gaming.
"We're also thrilled to provide even more value to our fans by enabling them to experience the best games of Xbox One, with an easy path to upgrade to Project Scarlett when it launches alongside Halo Infinite in Holiday 2020.
"This is just the start for Xbox All Access - we're excited to bring Xbox All Access to even more players and look forward to expanding the programme to more markets and retailers next year."
Last week, Microsoft's latest financial results showed a 7% drop in Xbox revenue, which the company said was due to a drop in console sales.
Earlier this month, the gaming giant also began the first public preview of its streaming service - Project xCloud - which allows gamers to play Xbox games on mobile devices such as smartphones and tablets for the first time.