Kyveli's place of birth is uncertain. Her mother was from Smyrna (Izmir), Asia Minor but at age 2 she was adopted out of an Athens orphanage by Anastasios and Maria Adrianou, a working class couple. She attended Hill School for Girls and did some reciting that earned her an award in 1901. At that point she was discovered by Konstantinos Christomanos who took her under his wing. Christomanos gave Kyveli her start in acting and became her teacher, mentor and second father.
By the 1920s, Kyveli took to acting in plays written mostly by Greek authors: Pantelis Horn, Grigorios Xenopoulos, Spiros Melas. She became the chief competitor of Marika Kotopouli the other great Greek stage actress of that era. Their antagonism is not limited to the acting arena: Kyveli was a Venizelist, Kotopouli a conservative. However, the two legendary actresses were forced to join forces to compete with the National Theatre: They played G.B. Shaw, O' Neill and Schiller.
Kyveli had been married three times:
- First to Mitsos Myrat (1903 - 1906) with whom she had two children, Alexandros and actress Miranda.
- To Kostas Theodoridis with whom she had a daughter, Aliki.
- To Georgios Papandreou the politician and future Prime Minister of Greece. They had a son, Giorgos, half-brother to Andreas Papandreou. The couple lived apart shortly after the Second World War but never divorced. When Papandreou died in November of 1968, it was Kyveli who paid all the funeral expenses.