Amazon has struck a deal said to be worth $40m (£30m) for the exclusive UK TV rights to the US Open tennis tournament, as the US firm looks to add to its 100 million Prime subscribers.

Amazon, which is in talks with the Premier League to potentially stream matches from 2019 to 2022, has struck a five-year deal starting with this summer’s tournament at Flushing Meadows in New York.

It will be provided to subscribers to its Prime service, which costs £79 a year and includes access to the streaming of music, films and TV shows such as The Grand Tour, plus free delivery of DVDs, CDs and books and other items purchased from Amazon.

Securing the rights to one of the four tennis grand slams adds to Amazon’s £50m, five-year, deal for the UK rights to the ATP World Tour, the men’s global competition featuring Roger Federer, Rafael Nadal and Andy Murray, for which it outbid Sky.

“We are proud to add the US Open to the growing portfolio of sports available on Prime Video,” said Alex Green, managing director of channels and sports for Amazon’s Prime Video operation in Europe. “This makes Prime Video a destination for tennis fans.”

The deal means that Amazon can provide Prime Video subscribers with access to three of the four grand slams. Subscribers who pay to access additional channels can also watch Eurosport, which has the UK rights to the Australian and French opens.

Wimbledon is protected by regulations as a “listed event”, meaning it has to be available in the UK on free-to-air TV, with the BBC holding the TV rights.

In 2016, Sky Sports dropped its coverage of the US Open after 25 years, ending one of the longest major sports rights deals.

Amazon revealed this week that it has more than 100 million subscribers to its Prime service. Jeff Bezos, its chief executive, revealed the subscription numbers in his annual letter to shareholders. The service was first launched 13 years ago as a way of fostering customer loyalty.

“It’s a mind boggling number that serves as a key barometer to how big Amazon’s kingdom has become,” said Daniel Ives at the research group GBH Insights, which had previously estimated 92 million Prime subscribers.

Bezos said Amazon had shipped more than 5bn items to Prime members globally in 2017.

In digital service terms, Amazon lags behind its chief video streaming rival, Netflix, which has 125 million worldwide subscribers who pay on average £85 a year. But it bests both Spotify, with its 71 million paying members, and Apple Music’s 40 million in the music streaming sector. Amazon offers Prime subscribers access to a library of 2m tracks, with the option to take out a dedicated Amazon Music subscription adding another 38m to the total available songs.

While providing free one-day shipping in the UK or two-day in the US adds to Amazon’s costs, Ives estimated that Prime subscribers spend on average twice as much at Amazon than non-subscribers. “It has become a golden ticket for Amazon,” he said.

Prime has also spurred sales of Amazon’s smart speaker line, the Echo, and use of its digital assistant, Alexa, with which users can buy goods via voice, as well as its push-button Dash ordering system.

It is in the process of phasing out its existing loyalty programme in favour of Prime after its recent acquisition the US supermarket chain Whole Foods, and is offering two-hour delivery from stores to members.