The 35-year-old, who began his career in England at Sunderland, has scored 12 goals in 65 appearances for the Jets over the past five seasons.
"When you play professionally for as long as I have you see the highs and lows of football," Bridges said in a statement. "Thankfully I've been lucky enough to have great support around me throughout my career and I've loved and cherished every minute of it.
"Having the opportunity to play football for a living is something that I never took for granted and I'm extremely grateful for all the experiences I've had along the way.
"I've had five fantastic years at the Jets and that's a credit to all the fans, the players I've played alongside and the staff who have been here along the way. Everybody has made me feel so welcome and this is a place I can now call home."
Bridges has played for Leeds United, Newcastle United, Bolton Wanderers, Bristol City, Carlisle United, Hull City, Sydney FC and MK Dons throughout his career.
The forward will play his final home game at Hunter Stadium when Newcastle take on Adelaide United on Friday.