Alessandro Bastoni was born on 13 April 1999 in Casalmaggiore, Italy. Bastoni's father, Nicola, was also a footballer, who played as a left–back for Cremonese. At the age of 7, he joined the youth side of Serie A club Atalanta, where he progressed through various age groups to the Primavera side, where he established himself as a regular starter at the centre of defence. In Serie A, Bastoni remained as an unused substitute for the six games after Genoa until making his debut in a 1–0 win over Sampdoria on 22 January 2017, playing full 90 minutes. On 31 August 2017, Inter Milan announced the signing of Bastoni for €31 million, and on the same day, his loan at Atalanta for the next two seasons. Inter officially recalled defender Alessandro Bastoni early from his loan with Atalanta and renewed his contract until 2023 on 14 July 2018.