The US actress, 84, had been rushed to hospital with a suspected stroke.
Her son, Todd Fisher, said the stress of his sister's death had been too much for her and in her last words, she had said she wanted to be with Carrie.
US actress Bette Midler said Reynolds was "devoted to her craft" and that her death was "too hard to comprehend".
Actress Debra Messing said Reynolds, her on-screen mother in sitcom Will and Grace, had been an "inspiration".
"A legend of course," she wrote in a statement. "The epitome of clean-cut American optimism, dancing with Gene Kelly as an equal, a warrior woman who never stopped working.''
Actor Rip Torn, who worked with Reynolds in her Las Vegas stage show, said: "I was blessed to work with this remarkable woman for 45 almost 50 years. That makes for a very rare bond and unique relationship.
"She was generous to a fault, never caring who got the laugh from the audience. I will always love her."
Veteran comic actress Carol Channing agreed: "She was beautiful and generous. It seems like only yesterday she was having lunch here at the house and we were discussing the possibility of working together in a new show."
For Star Trek actor William Shatner, Reynolds was one of the last of the Hollywood royalty.
"It breaks my heart that she is gone," he wrote. "I'd hoped that my grieving was done for 2016.
Reynolds had been at her son's house in Beverly Hills - apparently discussing the arrangements for Carrie Fisher's funeral - when she was taken ill.
She was admitted to Cedars-Sinai Medical Centre suffering from breathing difficulties and her death was confirmed a few hours later. It is thought she suffered a stroke.
Carrie Fisher, renowned for her role as Princess Leia in the Star Wars series, had died aged 60 the day before, after spending three days in a Los Angeles hospital.
She never regained consciousness after suffering a massive heart attack on board a flight from London to Los Angeles on Friday.
Speaking to the Associated Press news agency about his mother, Todd said: "She's now with Carrie and we're all heartbroken.''
Celebrity news site TMZ reported that Reynolds cracked while discussing plans for Carrie's funeral with her son, telling him: "I miss her so much; I want to be with Carrie."
Some people talk about "broken heart syndrome", known more formally as stress cardiomyopathy or takotsubo cardiomyopathy. According to the British Heart Foundation, it is a "temporary condition where your heart muscle becomes suddenly weakened or stunned. The left ventricle, one of the heart's chambers, changes shape."
It can be brought on by a shock. "About three quarters of people diagnosed with takotsubo cardiomyopathy have experienced significant emotional or physical stress prior to becoming unwell," the charity says.
This stress might be bereavement but it could be a shock of another kind. There are documented cases of people suffering the condition after being frightened by colleagues pulling a prank, or suffering the stress of speaking to a large group of people. It's speculated that the sudden release of hormones - in particular, adrenaline - causes the stunning of the heart muscle.
This is different from a heart attack, which is a stopping of the heart because the blood supply is constricted, perhaps by clogged arteries.
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How does grief cause physical pain?
Reynolds was leading lady in a succession of major Hollywood musicals and comedies in the 1950s and 60s.
She rose to stardom with Singin' in the Rain, at the age of only 19.
She received a best actress Academy Award nomination for the 1964 musical The Unsinkable Molly Brown.
Her other films included 1973 animated film Charlotte's Web, in which she provided the voice for the eponymous spider.
In 2015 she was given a lifetime achievement award by the Screen Actors Guild. The award was presented to her by her daughter.
Reynolds married singer Eddie Fisher in 1955 and had two children, Carrie and Todd. The couple divorced in 1959 after news emerged of his affair with movie star Elizabeth Taylor.
Reynolds married twice more.
The actress has a sometimes strained relationship with her actress daughter, who wrote about it in her semi-autobiographical novel Postcards from the Edge.
The pair stopped speaking to each other for many years but became closer later in life.
In an interview last month with US radio network NPR, Fisher said her mother was "an immensely powerful woman" whom she admired "very much".
As people gathered to pay their respects to the actress at Hollywood's Walk of Fame, one couple, Jose and Daniela Barrera, appeared to speak for many after a year marked by celebrity deaths.
"It's just, you know, a sad time I guess," Jose told the Reuters news agency. "With the closing of the year and so many deaths in the year, it's just sad."
"It was so sad," added Daniela. "It was a shocker. I mean, what were the odds of this happening? It was incredible finding out, sad."
Debbie Reynolds, who starred opposite Gene Kelly in the 1952 musical Singin' in the Rain, has died a day after the death of her daughter, Carrie Fisher.