At least 166 people were killed when armed men attacked three luxury hotels, a railway station, a popular tourist restaurant and a Jewish centre during a 60-hour rampage in November 2008.
Judge M L Tahaliyani said he had no doubts that execution was the right punishment for Kasab.
"He should be hanged by the neck until he is dead," he said.
"I don't find any case for a lesser punishment than death in the case of waging war against India, murder and terrorist acts."
India has blamed the violence on the Pakistan-based Lashkar-e-Taiba group and elements in the Pakistani military.
Tahaliyani rejected arguments by Kasab's defence lawyer that he had committed the crime under duress and pressure from the Lashkar-e-Taiba.
The judge said Kasab joined the group on his own and trained to be a fighter.
"Such a person can't be given an opportunity to reform himself," Tahaliyani said.
KP Pawar, Kasab's defence lawyer, had asked for the minimum punishment of life in prison for his client.
Al Jazeera's Prerna Suri, reporting from the court in Mumbai, said the sentence would bring some sense of closure to Indians affected by the attack.
"People are happy. Some people are quite excited, saying they might even celebrate on the roads soon enough," she said.
But she also noted that many people saw Kasab as simply a "footsoldier".
"The real perpetrators that India has singled out, based on Kasab's confession, is Lashkar-e-Taiba, the extremist anti-India group.
"What people here are saying is that it's not enough to hang Kasab. [They also want to see] the masterminds behind these attacks tried."
Outside the court Ujjwal Nikam, the public prosecutor, brandished a poster showing Kasab behind a noose and flashed victory signs to reporters.
"Today's sentencing sends the message that keeping Kasab alive would be a crime in itself," Nikam said.
"Terrorism and terrorists like Kasab cannot be tolerated. The death penalty is the only option."
Hamid Khan, who was severely injured when a taxi he and his mother were standing near was blown apart by a bomb planted in it by the attackers, said Kasab deserved to be executed.
|Some Indians were celebrating Kasab's death sentence on Thursday [AFP]
"His hands and legs should be cut and he should be left to suffer. My mother and I have been handicapped and we have suffered so much because of him," he said.
'[His punishment] will send a message to Pakistan or any other country," he said.
Deven Bharti, a senior police official involved with the investigation into the attacks, said: "We're all very satisfied. I hope it will be a deterrent for Pakistan so they will stop exporting terrorists across the border."
Kasab can appeal against the judgement in superior courts before moving a mercy petition to the president, a process that can take years.
The special prosecutor in the trial said on Wednesday that he expected it would take at least a year for Kasab to be executed.
Only one person has been executed in India since 1998 - a man convicted of raping and murdering a 14-year-old girl.
Many convicts simply wait in jail as their death sentence effectively becomes life in prison.
Those convicted over the 1991 assassination of Rajiv Gandhi, the former prime minister, and a 2001 attack on India's parliament, have yet to be executed.