Born in Livorno, Picchi started his career by playing for A.S. Livorno Calcio. In 1959 he moved to SPAL, before later at the peak of his time, and most of his career, at Milanese powerhouse F.C. Internazionale Milano.
A versatile defender, Picchi started to play in Internazionale as a right back, a role he previously held at SPAL. During the course of 1961–62 season, the legendary Grande Inter coach Helenio Herrera experimented by placing him as a libero. The new position was successful; he became an important figure in the team's strong defence, and indirectly set examples for teammates Tarcisio Burgnich and Giacinto Facchetti with his leadership. During that time, Internazionale was still captained by Bruno Bolchi. and the coach Helenio Herrera When Bolchi moved to Verona, Picchi was then selected as team captain. It was in his captaincy that Internazionale evolved into the era famously known as Grande Inter, when they won three scudetti, two European Champions Cups and two Intercontinental Cups in the 1960s.
Later career
After his time at Inter, he played for two seasons at Varese before retiring in 1969, at the age of 34.
A quick, versatile, and tenacious defender, Picchi began his career playing as a forward or as a central defensive midfielder, before being moved to right back, where he excelled, but later came into his own in the libero role. Picchi was primarily an old-fashioned sweeper, who was mainly known for his defensive skills, strong physique, and ability to win back, intercept and clear loose balls as a last man, while he was not particularly good in the air, due to his small stature; despite his more traditional, defensive-minded interpretation of the role, he was, however, also occasionally capable of getting forward, and of carrying the ball out into midfield, or starting plays from the back-line, due to his good technique and ability to read the game. Regarded as one of Italy's greatest defenders, and as one of the best sweepers of his generation, he was highly regarded for his tactical intelligence as well as vocal leadership on the pitch, and was known for his ability to organise the back-line and motivate his teammates.
Coaching career and death
After his playing career was over, Picchi pursued a coaching career in 1969; he went on to coach Varese, Livorno, and then Juventus, until 16February 1971, when he was hospitalised because of cancer, which ended his coaching career prematurely. He died three months later, at the age of 36, due a tumour in his sixth left rib.