No details were provided in a tweet by spokesperson Roberto Cuillo.
Sassoli, a 65-year-old socialist, had been hospitalised since December 26 due to abnormal functioning of his immune system, Cuillo said in a statement released the day before Sassoli's death on Tuesday.
"This hospitalisation was necessary because of a serious complication due to a dysfunction of the immune system," the statement said.
Sassoli had been struggling for months with poor health yet stayed on the job, where his vigour and easy smile were a trademark.
He was at his strongest when he took up the cause of migrants who died crossing the Mediterranean or dissidents such as Alexei Navalny, who is taking on the Kremlin from a jail cell.
EU Council President Charles Michel called him a "sincere and passionate European. We already miss his human warmth, his generosity, his friendliness and his smile."
Sassoli came to lead the legislature in 2019 following an intricate bout of political infighting among EU leaders which also saw German Christian Democrat Ursula von der Leyen become EU Commission President and Belgian free-market liberal Michel take the job as EU Council president.
Even if he was often overshadowed by von der Leyen and Michel, Sassoli led an institution which has become ever more powerful over the years and has become instrumental in charting the course of the European Union in many sectors, be it the digital economy, climate or Brexit.
The European Parliament represents the EU's 450 million citizens and refers to itself as "the heart of European democracy." It has more than 700 members directly elected by its member nations.
"I am deeply saddened by the terrible loss of a great European & proud Italian," von der Leyen said on Twitter.
"David Sassoli was a compassionate journalist, an outstanding President of the European Parliament and, first & foremost, a dear friend."
He was just as respected in Italy. The head of Italy's Democratic Party and a longtime friend, Enrico Letta, praised Sassoli's European passion and vision and vowed to carry them forward, though "we know we're not up to it."
In a tweet, Letta called Sassoli "someone of extraordinary generosity, a passionate European" and a man of "vision and principles, theoretical and practical."
Sassoli was first elected to the European Parliament in 2009. He won another term in 2014 and served as its vice president. He started out as a newspaper journalist before entering broadcasting as a high-profile presenter in Italy. It was a stepping stone for his political career.
He had considered running for the second part of the five-year term which starts next week, but decided not to run for reelection when lawmakers choose their new president in Strasbourg, France.
Roberta Metsola, the Christian Democrat who was already set to take over from Sassoli next week, said "I am heartbroken. Europe has lost a leader, I have a lost a friend, democracy has lost a champion."Â
She said Sassoli "dedicated his life to making the world a better, fairer place."
