By having Head caught in the deep 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, the other active bowler in this group, are the only quicks to have taken 600 Test wickets.
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 for the landmark wicket, with left-hander Head hooking a bouncer and Joe Root holding a low catch as he came in off the boundary at fine leg.
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.
Broad's double strike on Wednesday also saw him overtake Ian Botham as England's leading Test bowler against Australia with 150 wickets.
Broad, the son of former England batsman Chris Broad, made his Test debut against Sri Lanka at Colombo in 2007 under the captaincy of Michael Vaughan.
The then Leicestershire seamer -- Broad now plays for Nottinghamshire -- had only started bowling relatively late in a school career as a promising batsman.
But at international level he has become renowned for his match-winning spells, 20 times taking five or more wickets in an innings.
Three times he has taken at least 10 wickets in a Test, with his ability to generate late seam movement often proving too much for the world's leading batsmen.
The most celebrated return of Broad's career was his outstanding 8-15 at Trent Bridge during England's 2015 Ashes triumph in a match that Anderson missed because of injury.
Broad also scored a superb 169 against Pakistan at Lord's in 2010 before his batting regressed after he had his nose broken by a bouncer from India's Varun Aaron four years later.
Broad, whose wickets have come at an economical average of just over 27 apiece, is also the only England bowler to have taken two Test hat-tricks.
The first came against India in 2011 during a haul of 6-46, with the second against Sri Lanka in 2014.
