"My heart is broken as I cannot imagine our lives without him," wrote his wife Amanda Kloots on Instagram.
Cordero was nominated for a Tony for his role in Bullets Over Broadway and appeared in Waitress and A Bronx Tale.
While in hospital he suffered sepsis infections and mini-strokes and had his right leg amputated.
In May, his wife revealed he had woken from a medically induced coma but remained "extremely weak".
In a post confirming his death, Kloots said: "God has another angel in heaven now. My darling husband passed away this morning. He was surrounded in love by his family, singing and praying as he gently left this earth."
Kloots remembered her husband as "a bright light" who was "was everyone's friend".
She paid tribute to his "extraordinary" doctor and thanked everyone for "the outpour of love, support and help we've received".
While Cordero was in hospital, Kloots regularly sent him videos of her and their one-year-old son, Elvis, and encouraged fans to take part in a daily sing-a-long.
A fundraising page to help pay for medical expenses raised more than $600,000 (£480,000).
Oscar-winning actress Viola Davis led the tributes on Twitter writing: "My condolences to you Amanda who fought and loved so hard... so sorry for his little one. My heart is with you."
"My heart is broken," added actor Josh Gad. "I feel ill. Along with the entire Broadway community and the entire world, I mourn the loss of the incredible Nick Cordero."
Priscilla Presley tweeted: "I'm so shocked to see the news today that Nick has passed. My heart and soul goes out to Nick Cordero's beautiful wife and family. Rest In Peace, Nick."
"I can honesty tell you I have never met a kinder human being," said Scrubs star Zach Braff. "Don't believe that Covid only claims the elderly and infirm."
"It is so shocking and devastating to see one of your own come down as hard as he did," wrote Little Women star Florence Pugh on Instagram.
Cordero's TV credits included Law & Order: Special Victims Unit, and he had a role in the 2017 film Going in Style, which starred Morgan Freeman, Michael Caine and Alan Arkin.
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