By having Head caught hooking to Joe Root at fine leg for 48, the 37-year-old paceman joined Sri Lanka's Muttiah Muralitharan (800), Australia's Shane Warne (708), England's James Anderson (688) and India's Anil Kumble (619) in an exclusive club.
Broad and Anderson are the only fast bowlers to have taken 600 Test wickets.
Broad, the son of former England batsman Chris Broad, started this match, his 166th Test, on 598 wickets.
But after England captain Ben Stokes won the toss and elected to field on Wednesday, Broad struck an early blow when he had Usman Khawaja lbw for three to leave Australia 15-1.
He had to wait until his 11th over of his innings for the landmark wicket, with left-hander Head hooking a bouncer and Root holding a low catch as he came in off the boundary.
Head's exit left Australia on 189-5 as England, 2-1 down with two Tests to play, chase the win they need to maintain their hopes of regaining the Ashes.
