His representatives said in a statement that he "passed away peacefully" on 21 January in Las Vegas, aged 68.
The comic won an Emmy in 2016 for his role as Christine Baskets in comedy drama Baskets, plus two nominations for outstanding supporting actor.
He also co-created and starred in the cartoon sitcom Life With Louie.
Anderson based the show on his childhood, and also hosted popular US game show Family Feud for a number of years.
As well as having a role in 1988 romantic comedy film Coming to America, starring Eddie Murphy, the comic also appeared in its sequel last year.
He starred alongside Zach Galifianakis and Martha Kelly in FX show Baskets, and guest-starred on Big Bang Theory spin-off Young Sheldon, as well as playing a recurring character in the TBS dark comedy Search Party.
The comic was also a best-selling author, and his books included Dear Dad, which explored his relationship with his alcoholic father, and Goodbye Jumbo...Hello Cruel World, in which he wrote about his struggle with food addiction and self-esteem.
He paid tribute to the enduring influence of his late mother in his 2018 book Hey Mom.
Actor and writer Henry Winkler said: "Your generosity of spirit will cover the world from above."