Dutt, the son of a Hindu father and Muslim mother, who were both well-known actors, has insisted he was only armed to protect his family as he was worried about riots breaking out between Hindus and Muslims in Mumbai.
Dutt did not comment as he left court. Satish Maneshinde, his lawyer, called the verdict a vindication.
Maneshinde said: "Sanjay wishes his dad was alive to see that the family name is cleared. The judge has clearly said he had no knowledge of and was in no way involved in any terrorist act.
"The stigma and accusation that he is a terrorist is not there anymore."
Dutt could face up to three years in prison but has already served 18 months.
Sentences will be handed down after all the verdicts are delivered, expected to take two more weeks.
Entertainment industry colleagues of Dutt welcomed the verdict.
Filmmaker Karan Johar said: "It's so heartening to hear the verdict is out and he's not been convicted under any kind of conspiracy. We always knew he was innocent."
Lengthy detentions in jail on charges alone and no conviction are common in India's court system.
|Sanjay Dutt was only convicted of one minor charge unrelated to terrorism|
Half of Dutt's 105 movies were made after his release on bail in 1995.
Dutt's trial has transfixed Bollywood - the world's largest film industry by volume and ticket sales - where millions of dollars are riding on movies already under production.
Five other people were also convicted of involvement in the bombings on Tuesday.
The special court in one of the world's longest-running trials has found 86 people, mostly Muslims, guilty among 123 accused in the blasts in which 257 people died.
The attacks have been blamed on India's most-wanted man, Dawood Ibrahim, believed to be in Pakistan.
allegedly masterminded by the city's Muslim-dominated underworld at the time, in revenge for fatal Hindu-Muslim religious clashes a few months earlier.
Kode has also acquitted 23 others since he began issuing rulings in September.