Glatzer died on Tuesday in LA, said The Hollywood Reporter.
His death came less than three weeks after Moore won the best actress Oscar on February 22 for her performance as a woman with early-onset Alzheimer's.
Despite the severe limitations brought on by ALS, he completed the Oscar-winning film with his husband, Wash Westmoreland.
Glatzer was taken by ambulance to an LA hospital due to severe respiratory problems, two days before the ceremony. He and Westmoreland planned to watch the Oscar telecast from the hospital.
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At the end, Glatzer was able to "speak" only by tapping the big toe of his right foot on a specially designed iPad.
"I am devastated. Rich was my soulmate, my collaborator, my best friend and my life. Seeing him battle ALS for four years with such grace and courage inspired me and all who knew him.
"In this dark time, I take some consolation in the fact that he got to see 'Still Alice' go out into the world. He put his heart and soul into that film, and the fact that it touched so many people was a constant joy to him," Westmoreland said in a statement.
Born in New York, Glatzer came to LA to produce the daytime TV show "Divorce Court" and, using that experience, wrote and directed "Grief" (1993), which featured Illeana Douglas in a story about a sleazy daytime show.
Glatzer also produced the Tyra Banks' reality show "America's Next Top Model".
Besides Westmoreland, Glatzer is survived by his sister, Joan, and her husband, David, his nieces and nephews, and his daughter, Ruby.
"And finally, to our filmmakers, Wash Westmoreland and Richard Glatzer, who had hoped to be here tonight but they can't because of Richard's health. When Richard was diagnosed with ALS, Wash asked him what he wanted to do. Did he want to travel? Did he want to see the world? And he said that he wanted to make movies, and that's what he did.