Former tennis great, 70-year-old King, who won 39 grand slam titles, was moved to hear of Baltacha's death and said on her Twitter account: "Saddened to hear about Elena Baltacha's passing.
"My fondest memory w/Bally was sharing a wonderful chat when we met the Queen at @Wimbledon."
Another former world number one, Chris Evert, who won 18 grand slam singles championships and three doubles titles in the 1970s and 80s, wrote on Twitter: "Rest in Peace, beautiful Elena Baltacha...No words...Thoughts and prayers..."
Great Britain Fed Cup team-mate Laura Robson tweeted: "Impossibly sad. Forever a teammate. Sweet dreams Bally."
Other fellow professionals also paid tribute to the 30-year-old, who had dealt with a liver condition - primary sclerosing cholangitis - diagnosed at the age of 19, throughout her career with medication and regular blood tests.
Despite the disruption it caused, she went on to win 11 singles titles, reached the third round of Wimbledon in 2002 and the same stage of the Australian Open in 2005 and 2010.
Serbia's Ana Ivanovic tweeted: "So sad to hear about Elena. Tragic. My thoughts and prayers are with family... #RIPBally."
Kirsten Flipkens told her Twitter account: "Such a sad news to wake up with :-( R.I.P Elena Baltacha.. My thoughts and condolence go out to her family.. #notfair."
World number four Victoria Azarenka tweeted: "RIP Elena Baltacha...My thoughts and condolences to her family! what a tough loss for tennis world."
Kim Clijsters said on her account: "So sad to wake up to the terrible news of Elena passing away! RIP Bally! Thinking about her loved ones ..."
Wimbledon 2012 champion Petra Kvitova told her account: "Just woke up in Madrid. So sad to hear the news about Elena Baltacha :( RIP."
Current world number 49 Svetlana Kuznetsova tweeted: "I have nothing to say, so empty.. RIP Elena... Not fair ...my thoughts goes to her family .. She was such a beautiful person .."
Baltacha's former coach Jo Durie, a two-time grand slam champion in mixed doubles, hailed the Scot as a "fighter".
"She fought on the tennis court and she had problems she had to fight for the rest of her life," Durie said on Sky News.
"She didn't find out about the condition until she was about 19, she had to fight through that as well but she always took such a positive view of everything.
"She was just a fighter, I think that's what everyone would say about Bally."
Durie added: "It's just awful, I think we're all just so shocked that it happened so quickly, she'd just set everything up. Things were looking great and it just happened so quickly, we're all so shocked."
British number three Heather Watson left a tribute to Baltacha on Twitter, which read: "We've lost our lovely Bally, too young. Rest in peace. My thought are with Nino and all of her family xx."
Denmark's world number 14, Caroline Wozniacki tweeted: "So sad to hear about Elena Baltacha! RIP! Thoughts go out to her family and loved ones!"
Last year's Wimbledon champion Marion Bartoli admitted on her Twitter account: "I have no worlds to describe my sadness. RIP @ElenaBaltacha."