"In my memory, she will always be vibrant and young. Gone too soon. Sending my thoughts and prayers to Amanda's family," the former "Grey's Anatomy" star posted on Twitter.
He and Peterson co-starred in the 1987 film "Can't Buy Me Love," in which Dempsey played a high school nerd who pays a cheerleader (Peterson) to pretend to be his girlfriend.
Photos: Peterson and Dempsey together in "Can't Buy Me Love"
Patrick Dempsey pays tribute to 'Can't Buy Me Love' co-star Amanda Peterson
CAN'T BUY ME LOVE (1987) PATRICK DEMPSEY, AMANDA PETERSON CBM 001
CAN'T BUY ME LOVE (1987) PATRICK DEMPSEY, AMANDA PETERSON CBM 008
CAN'T BUY ME LOVE (1987) PATRICK DEMPSEY, AMANDA PETERSON CBM 005
CAN'T BUY ME LOVE (1987) AMANDA PETERSON CBM 002FOH
EXPLORERS (1985) ETHAN HAWKE, JASON PRESSON, RIVER PHOENIX, AMANDA PETERSON JOE DANTE (DIR) 005
A YEAR IN THE LIFE (MINISERIES) -- Pictured: (back l-r) David Oliver as Sam Gardner, Julie Ronnie as Lisa, (middle row l-r) Morgan Stevens as Jack Gardner, Adam Arkin as Jim Eisenberg, Jayne Atkinson as Lindley Gardner Eisenberg, Eva Marie Saint as Ruth Gardner, Richard Kiley as Joe Gardner, Wendy Phillips as Anne Gardner Maxwell, Scott Paulin as Glen Maxwell (front row l-r) Amanda Peterson as Sunny Sisk, Trey Ames as David Sisk -- (Photo by: Paul Drinkwater/NBC/NBCU Photo Bank)
A YEAR IN THE LIFE (SERIES) -- 'Things You Should Know Before and After' Episode 102 -- Pictured: Amanda Peterson as Sunny Sisk -- (Photo by: Ron Batzdorff/NBC/NBCU Photo Bank)
CIRCA 1989: Actress Amanda Peterson and actor Christopher Atkins on the set of the Columbia Pictures movie 'Listen to Me' circa 1989. (Photo by Michael Ochs Archives/Getty Images)
BEVERLY HILLS, CA - MAY 3: Amanda Peterson attends the premiere of 'Listen To Me' on May 3, 1989 at the Academy Theater in Beverly Hills, California. (Photo by Ron Galella, Ltd./WireImage)
Peterson's final credits include the 1989 Kirk Cameron-Jami Gertz drama "Listen to Me," a 1990 appearance on Neil Patrick Harris' star-making sitcom "Doogie Howser, M.D." and a 1994 film called "WindRunner."
She left the business in the early 1990's and returned home to Greeley, Colorado, where she was found dead. The cause of death was not immediately known. According to media reports, Peterson had been missing since July 3, and her father speculated about preexisting medical conditions as possible factors in her death.