The six men and a woman were members of the Sri Lankan Tamil Tiger rebel group.
The move came a day after the Supreme Court commuted the death sentences of three of the convicts, citing delays in deciding their mercy pleas.
Gandhi’s murder in May 1991 was seen as retaliation for the sending of Indian peacekeepers to Sri Lanka in 1987.
The decision to free the prisoners was taken on Wednesday morning at a cabinet meeting chaired by Tamil Nadu Chief Minister J Jayalalitha.
Ms Jayalalitha told the state assembly later that the government would send the cabinet decision to the federal government for approval.
“If there is no reply within three days from the centre, the state government will release all the seven… in accordance with the powers vested with the state government,” she said.
Among the prisoners to be released are the three men whose death sentences were commuted on Tuesday by the Supreme Court – Murugan, Santhan and Perarivalan. They have been in jail for more than 20 years and on death row since 1998.
The court ruled that they should be spared the death sentence as it was inhumane to keep them for so long under the threat of execution.
Nalini Sriharan, an Indian Tamil woman who will also be released, was also given the death penalty by the trial court in 1998, but the authorities commuted this to life imprisonment in 2000.
Three other convicts – Robert Pious, Jayakumar and Ravichandran – who are serving life sentences for involvement in the assassination would also be among those freed, authorities said.
There is sympathy for the prisoners in Tamil Nadu, where many believe that they were duped into taking part in a conspiracy they knew little about.
Governments in the state have long campaigned for clemency for the convicts, and correspondents say that with general elections due in India soon, Ms Jayalalitha will use the issue to win the support of ethnic Tamils for her party.
Among the prisoners to be freed are Murugan and his wife, Nalini Sriharan
Meanwhile, relatives have welcomed the prospect of the prisoners’ release.
Perarivalan’s mother was quoted by the Press Trust of India as saying she was “very happy” and she praised the Tamil Nadu chief minister for putting an end to “the pain” of a mother.
Mr Gandhi was killed by a female suicide bomber at an election rally in Tamil Nadu. In 2006, the Tamil Tigers expressed “regret” for the murder.
A BBC correspondent in Delhi says the Gandhi family is unlikely to oppose the move to free the prisoners.
Nalini’s death sentence was changed into a life term following a plea for clemency by Mr Gandhi’s widow and Congress party president Sonia Gandhi. Mrs Gandhi had appealed on Nalini’s behalf because she had a young child.
In 2008, Gandhi’s daughter Priyanka Gandhi met Nalini in jail. “I needed to make peace with all the violence in my life,” she later said.
“I don’t believe in anger or violence and I refuse to let it overpower me. Meeting Nalini was my way of coming to terms with my father’s death,” Ms Gandhi said.