The match will form part of the build-up to the Australian Open, under new rules devised by Tennis Australia as they hope to provide a quicker-paced version of the sport.
There will be no advantage scoring, no service lets and tie-breaks at three games apiece in a best-of-seven sets format.
"The new format is a game changer and is set to revolutionise the game of tennis, particularly at club and social levels," said Tennis Australia chief Craig Tiley.
"Time today is precious and this new fast format is perfect for any player who wants to fit their tennis matches into a busy lifestyle.
"To have Roger and Lleyton, our own great Australian champion, showcase the format for the first time is not only special for Sydney and Australia, but for the sport around the world."
Federer, who helped Switzerland to their maiden Davis Cup triumph against France on Sunday, commented: "I can't wait to come to the beautiful city of Sydney for this very special match against my old friend and rival, Lleyton Hewitt."
Hewitt, meanwhile, added: "Playing Roger in this new format will be an exciting challenge for both of us and a lot of fun. It's a fantastic innovation for tennis, and one that I hope will take off."