He won 81 caps for the Wallabies in a 10-year international career and played 81 times for the Falcons after joining the Kingston Park side in 2004, scoring 430 points.
Burke said: "I thoroughly enjoyed my time in Newcastle, playing my rugby and closing out my career with the Falcons.
"I look back on my four seasons and hopefully say that I contributed to the team's performance and provided some enjoyment for the fans to come and watch.
"To have played week in, week out with what I thought was one of the best group of supporters of a club, gave me a great sense of pride, and over my time I'd hoped to have repaid them with my commitment to the shirt.
"Playing with some of the game's best talent certainly gave me motivation to continue my rugby and to keep contributing to the game.
"To have experienced the Guinness Premiership and the Heineken Cup, and the high standard of play, was a privilege to be part of."
Newcastle director of rugby Steve Bates, added: "I was fortunate enough to work with Matt this season before his injury, and it is not hard to see why he is held in such high esteem at the club.
"Even after suffering what must have been a devastating blow he remained an incredibly positive presence around the team.
"Whilst it is a great sadness that a fantastic playing career is now at an end, I'm sure everyone will join me in thanking Matt and wishing him all the best for the future."