Murray and Robson enjoyed a run to the final in the 2010 edition of the event.
Australia are represented by Lleyton Hewitt and Alicia Molik, though they are not amongst the seeds.
The Hopman Cup is a popular team event for top players to warm up for the Australian Open, and will begin on January 1 2011.
Matches at the Perth Arena are best of three, consisting of a men's singles, a women's singles and a mixed doubles. After a round robin group stage there are semi-finals and a final.
The draw means that Robson is pitted against Williams in a singles match as Great Britain try to negotiate a group which includes the USA , France and Italy.
1) Serbia – Ana Ivanovic and Novak Djokovic
4) Belgium – Justine Henin and Steve Darcis
Kazakhstan – Yaroslava Shvedova and Andrey Golubev
Australia – Alicia Molik and Lleyton Hewitt
2) USA - Serena Williams and John Isner
3) Great Britain – Laura Robson and Andy Murray
France – Kristina Mladenovic and Gael Monfils