The video sees the band portrayed as a gang called the Crooked Steps as they make their way around the streets of LA, dismissing dance DJs and putting on rollicking rock shows.
Rather than motorbikes, though, the leather clad group are mounted on segways, and are continually pursued by a cop played by Deadmau5 (who catches them in the end).
'By Crooked Steps' is the second single taken from the group's comeback album King Animal, which was released last November.
Grohl apparently approached the band with his idea, which was a winner from the start with the group.
"I had an idea," Grohl explains in a behind the scenes clip. "I got a copy of the record and the third song 'By Crooked Steps' was a signature, instantly recognisable Soundgarden song."
"Dave had the idea perfectly set up," admits Soundgarden's Ben Shepherd, "start to finish, right on."
"We were really surprised he found a sort of comedic element in this song becuase it's a kind of heavy serious kind of hard rock song," adds drummer Matt Cameron.
Watch the video for 'By Crooked Steps' below
King Animal was released last November and has received largely positive reviews from critics and fans.
But some might be slightly surprised that Grohl has managed to find time to direct the video.
Between making a documentary about Sound City Studios, forming a supergroup to provide the soundtrack for said documentary, returning to drum with Queens Of The Stone Age, oh, and knocking up a drum track from metallers Ghost's cover of ABBA's 'I'm A Marionette', you might think Grohl's schedule would be pretty full.
Watch the behind the scenes footage below
Below: Money or love? Why Soundgarden, Stone Roses are reuniting