UK newspaper The Guardian said Amazon has secured the rights in a five-year deal, from 2018 to 2022, for a fee of about $40m (€34m), or $8m per year.
The rights were previously held by international sports broadcaster Eurosport, which sublicensed the rights on to pay-television broadcaster Sky in the UK.
Three months ago, Amazon sealed its first major sports-rights deal in the UK by outbidding Sky for the men’s ATP World Tour in a five-year agreement from 2019 to 2023.
In May, Amazon struck a deal to offer Eurosport channels via its Prime Video subscription service in the UK.
With Eurosport having UK rights to the Australian Open and French Open and non-exclusive rights to Wimbledon, Amazon will be able to offer all four of tennis’ grand slams.