Ellis's manager, Emily Gerson Saines, confirmed the actor's death via an emailed statement on Saturday (local time).
The Hollywood Reporter, which was first to report Ellis's death, quoted her as saying the actor died from complications of heart failure, adding more information would come to light in coming days.
The Illinois-born actor, who studied at the famous New York performing arts school Juilliard, played the role of Lafayette on the HBO drama from 2008 to 2014, and more recently appeared in the CBS detective series Elementary. He was also a playwright and a director.
"Nelsan was a singular talent whose creativity never ceased to amaze me," True Blood creator Alan Ball told the Hollywood Reporter.
Co-star and Academy Award winner Anna Paquin tweeted her condolences, writing: "It was an utter privilege to work with the phenomenally talented and deeply kind soul.
"I'm devastated by his untimely death."
Actor Joe Manganiello who played the role of Alcide Herveaux alongside Ellis in True Blood wrote: "Crushed today by the loss of my friend and castmate Nelsan Ellis.
"He was a wonderful person, a pioneer, and a one-of-a-kind artist. RIP."
Ellis also appeared as Martin Luther King, Jr in Lee Daniels' The Butler, and his film resume included The Help and the James Brown biopic Get On Up.
LGBT community pays tribute
Ellis was slated to appear at Queer Expo, Australia's first-ever LGBT Pop Culture expo at the Melbourne Showgrounds next weekend.
"We are extremely heartbroken to hear this morning that our guest and the incredible actor and person, Nelsan Ellis has passed away," the organisers said on Facebook.
"We cannot express our sorrow and heartache at this news."
In a 2009 interview with Chicago's edition of Time Out magazine, the Chicago native told reporter Laura Hawbaker that despite identifying as a straight man, his conservative father did not approve of his role.
"Truth of the matter is, he don't want his son prancing around in lipstick and makeup, playing some gay dude," Ellis said.
But Ellis expressed a desire for his portrayal of Lafayette to resonate with people beyond the LGBT community.
"It's about accepting what's different," he said.
Fans have since taken to Twitter praising Ellis for his dimensional portrayal of a gay man of colour and his prominent involvement within the LGBT community.
"I dressed up as Lafayette once for Halloween and never have I felt so strong and beautiful. Characters like this are needed in my community," wrote one Twitter user.
While Selma director and activist Ava DuVernay said, "Rise in peace … you made a difference."
And the Gay and Lesbian Alliance Against Defamation (GLAAD) tweeted their condolences for their "friend" Nelsan Ellis.