Williams, 37, has not played since her controversial US Open final defeat by Naomi Osaka in September.
The 23-time Grand Slam champion partners Frances Tiafoe, while 20-time Grand Slam winner Federer and Belinda Bencic will seek to defend their title.
Cameron Norrie and Katie Boulter will represent Great Britain in Perth.
"The Aussie fans are always so warm and supportive and the Hopman Cup has always given me a great start to the season, especially ahead of the Australian Open," said Williams, who pulled out of this month's China Open.
Williams will be playing in Australia for the first time since winning the 2017 Australian Open while eight weeks pregnant, having missed last year's tournament as she was not fully fit to return following the birth of daughter Olympia.
The Hopman Cup runs from 29 December until 5 January, with the 2019 Australian Open taking place from 14-27 January.
The mixed team event features eight nations split into two groups, with teams facing each other in sessions that consist of a men's and women's singles match and a mixed doubles match.
Each team plays the other three in their group, and the top teams in each group then meet in the final.
The USA are due to meet Switzerland on New Year's Day in Group B, which also features Great Britain and Greece.
Group A consists of France, Spain, Germany and hosts Australia.
Federer, 37, and Bencic, 21, won Switzerland's first Hopman Cup since 2001 earlier this year.
France - Lucas Pouille and Alize Cornet
Spain - David Ferrer and Garbine Muguruza
Germany - Alexander Zverev and Angelique Kerber
Australia - Matt Ebden and Ashleigh Barty
Great Britain - Cameron Norrie and Katie Boulter
Greece - Stefanos Tsitsipas and Maria Sakkari
Switzerland - Roger Federer and Belinda Bencic
USA - Frances Tiafoe and Serena Williams