The versatile 22-year-old, who has the ability to play in a full-back role, has made 22 appearances for the Waratahs while he broke the try-scoring record when playing for the Wallabies at the World Rugby Under-20s Championship in 2014 with 10 in five appearances.
Kellaway will now move to the Premiership to link up with his former Waratahs' team-mate Taqele Naiyaravoro, who moved to Franklin's Gardens in February.
He said on the Saints' website: "Getting the chance to join Northampton Saints was a really exciting opportunity for me and one I jumped at.
"The club has a great history of success and their ambition is clear to see with Chris Boyd and the new coaching set-up coming in this summer, as well as the number of top-quality players also joining the club next year.
"I'm excited to get going and to pull on the black, green and gold jersey for the first time."