Burrows, who directed the US sitcom and was also the co-creator of Cheers, died aged 85, with his death announced on Friday.
In a post on Instagram, Schwimmer, 59, who played Ross Geller in Friends, said: "Jimmy Burrows brought out the best in every actor he ever worked with, and elevated every show he directed, making it funnier and more moving than anyone expected.
"His warmth, humility and generosity made us feel safe, like family, and I'm sure we weren't the only cast to feel that way. He looked out for us, on camera and off.
"He became another father figure for me, and I'm sure others.
"Paternal in the best sense of the word, loving, wise, encouraging, challenging, instructive, patient, inspiring, playful - and on my best days, I'd like to think, even proud."
Schwimmer said he was already missing the director, who he said he was "forever grateful to", and the post was accompanied by a black and white image of him, Burrows and LeBlanc.
LeBlanc, 58, who played Joey Tribbiani in Friends, said: "Jimmy, words cannot describe the impact and influence you had on us and everyone who was lucky enough to have known you.
"You sir are a true icon on so many levels. Well wishes in your next act. You will be missed. God bless."
Kudrow, 62, who played Phoebe Buffay in Friends, posted a picture of herself with Burrows next to his director's chair on her Instagram story.
In a statement announcing his death, shared with US outlet People, Burrows' family said: "As a legendary director, mentor, and creative force, he helped shape generations of comedy and brought immeasurable joy to audiences around the world."
Burrows also worked on shows including The Big Bang Theory and Will and Grace, and won 11 Emmy Awards during his career.
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