The 34-year-old, who has been a free agent since being released by Aston Villa in the summer, will join Newcastle for the 2012-2013 season, which begins in October.
He will be paired up front with the former Leeds forward Michael Bridges, who has been at the Jets since 2009.
The Newcastle coach, Gary van Egmond, said Heskey's relationship with Bridges had allowed him to gain an "understanding" of what the A-League has to offer.
"His effectiveness in being able to hold the ball up and invite other players to play off him is going to be a big benefit to us," he said.
"He's someone who can really lead the line and that is exactly what we've been missing."
Heskey said he was excited at the prospect of playing for a new club in a new country but also keen to make a wider contribution to football in Australia.
"I hope I can help grow football at the grass-roots level and also provide advice to young players at the Jets," he said.