The American actor, best know for his role in the movie Grease and TV series Babylon 5 has passed away at the age of 60.
Conaway first became popular alongside John Travolta and Olivia Newton-John in the 1978 musical film Grease.
In April, Travolta offered to support for the troubled actor to return to rehab, an offer which Conaway rejected.
My heartfelt thoughts are with his family and loved ones at this very difficult time, Travolta said in a statement.
On May 11, 2011, Conaway was discovered unconscious from what was initially described as an overdose of pain medication.
Conaway had been suffering from pneumonia and sepsis and was recovering from a latest surgery to relieve back pain. He had also fighting with drug and alcohol addiction.
On May 26, 2011, Conaway's family took off his life support after doctors said that there was no more they could do to save him.
Conaway died at 10:30 a.m. at a Los Angeles-area hospital. He was surrounded by his sisters, nieces and nephews.