Born in Naples, the daughter of a doctor and a teacher, Dell'Anna grew up between Castel Volturno and Giugliano in Campania. She studied at the Drama Studio London and the Guildhall School of Music and Drama.

After some minor roles, Dell'Anna had her breakout in 2012, when she played the twins Micaela e Manuela Cirillo in the Rai 3 soap opera Un posto al sole. In 2015 she landed her best known role, Patrizia Santore in the crime series Gomorrah. For her performance in Mario Martone's The King of Laughter, she got a David di Donatello nomination for Best Supporting Actress. She plays the lead role of Mother Cabrini in the 2024 film Cabrini, getting more exposure to English-speaking audiences.