"It's so very sad," Olivia said in a statement to E! News. "Jeff had a good heart and was so very talented. He was a big part of our family for many years and he will be missed."
Conaway was more than just a member of Olivia's on-set family during her Grease days, however. The former Celebrity Rehab star later married into her actual family in 1980, after Olivia introduced him to her sister, Rona.
Rona and Conaway, who have a son together, went on to divorce five years later.
Conaway died Friday in a Los Angeles-area hospital after he was taken off of life support. While he struggled publicly with substance abuse over the last decade, his cause of death has not yet been determined.