The iconic actor died on Saturday morning after a long battle with prostate cancer. He was 74.
Hopper was known for his roles in films including Easy Rider, Blue Velvet and Apocalypse Now.
Guitarist Slash tweeted: "You take the great ones for granted until they're gone. RIP Dennis Hopper."
Radio 1 DJ Zane Lowe also took to Twitter to offer his condolences.
"Dennis Hopper RIP," he wrote.