Marshall, who also created Mork & Mindy starring Robin Williams and directed hit films including Pretty Woman, The Princess Diaries, Beaches, and Valentine’s Day, died of complications from pneumonia after a stroke.
Winkler shot to fame playing the rebellious Arthur ‘Fonzie’ Fonzarelli in the family comedy and has said he owes Marshall his career.
He wrote on Twitter: “Garry Marshall Rest In Peace... Thank you for my professional life. Thank you for your loyalty, friendship, and generosity.
“Larger than life, funnier than most, wise and the definition of friend.”
Marshall died in hospital in Burbank, California, on July 19, said his publicist, Michelle Bega.
Director Ron Howard, who starred in Happy Days as the clean-cut Richie Cunningham, said he missed Marshall already, writing: “RIP #GarryMarshall whose humour & humanity inspired. He was a world class boss & mentor whose creativity and leadership meant a ton to me.
“Garry’s mantra, to those who succeeded in entertainment was simple ... ‘Life is more important that show business’.
“I miss Garry already. He leaves a huge void for all who were lucky to be in his orbit. A great friend.”
Goldie Hawn, who starred opposite her partner Kurt Russell in Marshall’s film Overboard, wrote: “Our beloved Gary Marshall has passed! He was so special to our family and we will miss his gift of true joy and love!
"Thank you Gary for Overboard and all the films you made that had humanity, humour and goodness that lifted our spirits. God has you now. Rest dear one. We love you.”
Ashton Kutcher, who starred in Marshall’s films Valentine’s Day and New Year’s Eve, paid tribute, saying: “I lost a friend & mentor. We lost a beautiful man & masterful story teller. Gary Marshall I love you. I hope I get to go where you are.”
Topher Grace, who also starred in Valentine’s Day, wrote: “Oh man, this is a tough one. Honoured I spent time with this kind man. My love to his wife and family. #garrymarshall.”
Marshall, who was a former journalist, first found success in 1970 when he and his writing partner turned the Broadway show The Odd Couple into a TV series.
His first big screen success was Pretty Woman, starring Julia Roberts and Richard Gere, in 1990. The film was such a hit the pair reunited for Runaway Bride in 1999.
He also made appearances on screen in supporting roles such as a casino boss in Albert Brooks’ 1985 film Lost In America. and interfering network boss Stan Lansing in 90s comedy Murphy Brown.