Williams, 63, hung himself Monday morning after years of battling depression and substance abuse.
At a Manhattan press conference to promote The Giver Tuesday morning, Bridges offered a stirring, heartfelt tribute to Williams.
Bridges and Williams co-starred in the 1991 movie The Fisher King, playing respectively a suicidal radio star and a delusional homeless man on the quest for the mythical Holy Grail.
"I just want to acknowledge the fullness of life -- the joy and the sadness that is in store for us all and I am filled with both today, as I was last night, learning of my dear friend's passing. Robin. And the wonderful, joyous feeling of giving birth to our child here. The Giver. The combination was just quite remarkable," the 65-year-old actor told the assembled journalists, many of whom had also interviewed Williams over the years and were clearly shaken by his death.
Bridges went on to say he was filled with happy memories of Williams as he pulled up in his car to the Central Park Boathouse where the after-screening party for The Giver was held Monday night.
"I'm sitting there with my wife, trying to gather myself, and I look out the window and I say: 'What? Is that Robin? Is that his ghost? No, it's Radioman!'" Bridges laughed, referring to the scruffy New York personality who frequently shows up uninvited to celebrity events, wearing a boom box around his neck. Radioman is so well-known he has even appeared as himself in numerous TV shows and films.
"It brought back all of these wonderful feelings of what an amazing time [Robin and I] had together here in New York shooting The Fisher King," Bridges added.
"I got out of the car and I embraced Radioman and I looked at his face and I remember when we were shooting The Fisher King... Radioman, you know, he knows where all the movies are shot somehow. I don't know how he magically does that, but I remember us seeing Radioman.
I embraced Radioman [Monday night] and I felt Robin's spirit, as I am feeling it now in this room with us and just before I came down [to the ballroom of the Essex House hotel] I was looking out my window at Central Park -- my favorite part about New York -- and I am remembering the last scene [in The Fisher King] of me and Robin out there at 4 o'clock in the morning. Nude. Naked. And Robin was just wild and free. He says, 'Let the wild pony dance!' And rubbing his butt on the grass and he says: 'You know why dogs do this? Because they can!' He was just so wild. And, so, I just had to share that with you because that's what is going on so strongly and how much I miss him. I'm sure you guys do, too. What a gift he was to all of us."
Williams won an Oscar for his performance in Good Will Hunting. His other films include Awakenings, Good Morning Vietnam, Mrs. Doubtfire, Dead Poets Society, Hook, The Birdcage, What Dreams May Come, Aladdin, Nine Months, RV, August Rush and the Night at the Museum franchise. He is survived by his third wife and three adult children.