Drogba is a member of the Bété people. He was born in Abidjan, Ivory Coast, and at the age of five was sent to France by his parents to live with his uncle, Michel Goba, a professional footballer. However, Drogba soon became homesick and returned to Abidjan after three years. His mother nicknamed him "Tito", after president Josip Broz Tito of Yugoslavia, whom she admired greatly. He played football every day in a car park in the city, but his return to the Ivory Coast was short-lived. Both of his parents lost their jobs and he again returned to live with his uncle. In 1991, his parents also travelled to France; first to Vannes and then, in 1993, settling in Antony in the Paris suburbs, at which point the 15-year-old Drogba returned to live with them and his siblings. It was here that he began playing team football more frequently, joining a local youth side. Drogba then joined the semi-professional club Levallois, gaining a reputation as a prolific scorer in the youth team and impressing the coach with his professional attitude. His performances earned him a place in the senior squad but despite scoring in his debut, the 18-year-old Ivorian failed to make an impression on Jacques Loncar, the first team coach.

When Drogba finished school he moved to the city Le Mans to study accountancy at university and changed clubs, becoming an apprentice at Ligue 2 club Le Mans. However, his first two years there were marred by injuries and he was physically struggling to cope with the training and match schedule. Former Le Mans coach Marc Westerloppe later remarked that "it took Didier four years to be capable of training every day and playing every week". Furthermore, Drogba had never attended a football academy and only began daily football training as an adult.

By age 21, Drogba realised that he had to establish himself as a player soon or else he would have little chance of becoming a professional footballer. He made his first team debut for Le Mans soon thereafter and signed his first professional contract in 1999. The same year, he and his Malian wife Alla had their first child, Isaac. He grew into his new responsibilities, later stating: "Isaac's birth was a turning point in my life, it straightened me out". His first season, in which he scored seven goals in thirty games, boded well for the future, but during the following season he did not live up to expectations. Drogba lost his place to Daniel Cousin due to injury, then upon his return, he failed to score throughout the remainder of the season. However, he returned to form the following season, scoring five goals in 21 appearances.