King will join the Victorian club from next season after six seasons with the Knights, first making his NRL debut with the club in 2016.
The Knights prop will add great depth to the Storm's forward pack, with his arrival prompting excitement from club football boss Frank Ponissi.
"Josh displays a number of traits which we love at Storm, and look for in players we recruit, both with his on-field performance and his character and personality off the field," Ponissi said club's announcement.
“Tim (Glasby - Storm recruiter) had a close-up look at Josh as a teammate and liked what he saw.
“He’s a hard worker, committed to improving his game and as a middle forward, we expect that his best years are still to come.
“We’re very happy he’s committed to spending the next two years with us and pushing for a place in our top 17.”
King has played 74 games for the Knights, 14 coming this season as a key role player off the interchange.