He was 49.
"Slayer is devastated to inform that their bandmate and brother, Jeff Hanneman, passed away at about 11 a.m. this morning near his Southern California home. Hanneman was in an area hospital when he suffered liver failure," the band said in a statement posted on its website and Facebook page.
Hanneman leaves behind his wife, Kathy, a sister and two brothers.
"He ... will be sorely missed," the band said.
The guitarist was with Slayer from its founding in 1981. Its breakthrough came five years later with the release of "Reign in Blood," an album that included two songs -- "Angel of Death" and "Raining Blood" -- co-written by Hanneman.
That was one of 10 studio albums that the band put out over three decades together, during which they performed thousands of shows.
On Slayer's official website, Hanneman said that the last one -- "World Painted Blood" -- came together quickly because the band's members worked seamlessly.
"The interaction between all of us on this record was really something special," he said. "... The chemistry was just good."
In 2006 and 2007, Slayer won Grammy awards for best metal performance.
News of Hanneman's spurred thousands to comment about him on Slayer's Facebook page.
Wrote one: "One of the best shredders ever to walk Earth. RIP, good sir."