Williams was found dead in his California home Monday at age 63.
"I just want to acknowledge the fullness of life -- the joy and the sadness that is in store for us all," Bridges said.
"He was an amazing man," Bridges said of his former co-star. The actor, who shared the screen with Williams in "The Fisher King" (1991), smiled as he shared a story of their time together on set.
"Just before I came down [here today], I'm looking out my window to Central Park, my favorite part about New York, and I remember the last scene of me and Robin out there at 4 o'clock in the morning nude -- naked!" he said. "Robin is just wild and free ... rubbing his butt on the grass, and he goes, 'You know why dogs do this?! Because they can!'"
"I just had to share that with you," Bridges added. "Because that's what's going on so strongly and how much I miss him ... and what a gift he was to all of us."
Sarah Michelle Gellar said the funny man was as gracious as he was gifted.
Gellar, who played Williams' daughter in the CBS comedy "The Crazy Ones," told People magazine that her life is "better" for knowing the actor: "To my children he was Uncle Robin, to everyone he worked with he was the best boss anyone had ever known, and to me he was not just an inspiration but he was the father I had always dreamed of having. There are not enough adjectives to describe the light he was, to anyone that ever had the pleasure to meet him. I will miss him every day, but I know the memory of him will live on. And to his family, I thank them for letting us know him and seeing the joy they brought him. Us crazy ones love you."
Her personal anguish was made poignantly evident at the end of her emotional statement: "God, grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference."
Lisa Jakub, Williams' co-star, who played his daughter, Lydia, in "Mrs. Doubtfire," also penned a touching letter in response to the news of his death.
"Robin Williams died today," she wrote of her blog. "It seems surreal to write that. ... Everyone is tweeting and Facebooking and calling in to radio shows about what a great talent Robin was. Yeah. He was. But that wasn’t what I adored about him. It was the fact that he was an incredibly kind human being."
She continued, "When I was 14 years old, I went on location to film 'Mrs. Doubtfire.'"
She said her school kicked her out because of the five months she would be on set filming.
"When I arrived at work the next day, Robin noticed that I was upset and asked me what was wrong," she wrote. "I explained what had happened, and the next day, he handed me a letter that he wrote to my school. He explained that I was just trying to continue my education while pursuing my career. He wrote embarrassingly kind things about my character and my work, and requested that they reconsider and allow me to return to my classes."
The school didn't let Jakub back in, but she could care less about that.