The star, who had a string of pop hits in the 1960s before presenting TV shows like Blind Date and Surprise Surprise in the '80s, died on Saturday, aged 72.
A book of condolence has been opened in her home city at Liverpool Town Hall.
Childhood friend Terry McCann said Black told him she knew she was going to die and her beloved late husband Bobby Willis was "waiting for me".
A post-mortem examination has been carried out. The results may not be officially published for several days or possibly weeks, but Spanish police have said the indications point towards natural causes.
BBC News correspondent Robert Hall - who is in the resort of Estepona where Black lived - said she was found on her balcony by her son who was staying nearby.
He said paramedics arrived at around 18:00 local time (17:00 BST) but were unable to save her.
Mr McCann said he had seen the star in Spain during the last year.
"I wasn't surprised when I found out she had died," he told BBC News.
"The last thing she said to me was she was going blind, she showed me her hands, she had arthritis," he said. "She willed herself to die. She said, 'Bobby's waiting for me.'
"Her mother went the same way. I don't know what her mother died of but it seemed she associated it with her mother's death and she just knew it was going to happen.
"She just said, 'Look at me, I'm a wreck.' I was trying to cheer her up. She knew something we didn't.
"She knew she was going to die and she said she wasn't going to linger like her mother.
"Her mother was ill for two years and she had the same complaint and she said she was never going to linger like that."
Liverpool City Council say that between 400 and 500 people have so far left messages in a book of condolence at the town hall, where the flag is also flying at half mast. The book will be open to the public until Friday.
Fans signing the book on Monday included:
Sylvia Lewis (above): "Occasionally I used to work on the cloakroom at the Cavern with her. One Saturday, when I wasn't [working], Cilla was the cloakroom girl. When it came to the end of the evening my coat had gone. Cilla had given it away to somebody else! I met Cilla at the Pride of Britain Awards every year and she always used to come up to me and say 'Girl, do you remember your coat? And we never found it, did we?'"
Ann Stalker: "I absolutely love her. She was an icon from my era. I just wanted to pay my respects. I wrote: 'Ta-ra Cilla. You were a credit to us all. Rest in peace.'"
Cheryl McFarlane: "She's somebody I remember so much and love very much. She's got a beautiful family and she was so wonderful to Liverpool. I just wanted to come and visit and say rest in peace."
Since Black's death, tributes have poured in from figures ranging from UK Prime Minister David Cameron to Sir Paul McCartney and Ringo Starr - who knew Black from the Merseybeat scene in the '60s.
Sir Paul described her as "a lovely girl who infected everyone with her great spirit."
TV presenter Gloria Hunniford said Black never really got over the "deep loss" of her husband in 1999.
"Bobby was wonderful. Wonderful as a manager and wonderful as a husband," Hunniford told BBC 5 live. "She was a one-boy girl and I don't think she ever got over the vacuum of the loneliness that Bobby left."
Actress Barbara Windsor said: "I've seen her twice in the last few weeks. As always she looked immaculate. But I knew she wasn't very well. She didn't seem very well."
Morrissey, who covered Black's single Work is a Four-Letter Word with The Smiths, also paid tribute.
"Never stationary throughout the 1960s, Cilla Black made some great records - The Right One Is Left, Suffer Now I Must, It's For You, I've Been Wrong Before, What Good Am I?
"I'm very grateful for the songs, and it never occurred to me that such people could die."
Mr McCann grew up near Black and her family on Scotland Road in Liverpool.
He discovered her vocal talents when they listened to music as youngsters.
"She used to play records and sing along with them. That's when I realised. I was working at a club called The Iron Door and coaxed her to get up and sing. That was the first time she sang in public.
"Everyone was surprised by how good she was but she was very, very nervous. Eventually her confidence grew later on."
Mr McCann arranged an audition for Black with EMI - but The Beatles' manager Brian Epstein later won her signature and took over as her manager.
Promoter Sam Leach put on the gig at The Iron Door and recalled how she ran to the toilets in tears afterwards.
"I'd realised how good she was," Mr Leach said. "She was like [gospel singer] Mahalia Jackson. So when she came out I said, 'You've got a lovely voice.'"
However, she said no when Mr Leach asked her to perform the following week. "She said, 'I'm not going to do it, I made a fool of myself,'" Mr Leach said. "I ignored that and put an advert in the [Liverpool] Echo."
She had little choice but to perform the next week, Mr Leach added: "She was brilliant. Absolutely fantastic. She gave me a big hug and said, 'Thanks, I should have listened to you.'
"That was the start of her career."
Cilla Black was ailing and "willed herself to die", according to a long-time friend.