"My plea to repeal AFSPA heard in Tripura. AFSPA withdrawn. Victory for sanity and humanity," Chidambaram wrote on microblogging site Twitter.
The senior Congress leader had strongly advocated, as Union Home Minister, for repeal of the Armed Forces (Special Powers) Act, 1958.
"Some things do not have a place in a civilised country. One of them is AFSPA," he had said recently.
Expressing concern over alleged abuse of the act leading to violation of human and democratic rights of locals resulting in their alienation, CPI said that what the CPI-M government had done in Tripura is the "right thing".
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"There has been the demand in North-East including Manipur that AFSPA be repealed. A similar demand has also been raised in Jammu and Kashmir.
"Over the years, use and abuse of the act has led to violation of human and democratic rights and led to alienation of local people. The new situation demands that Centre should review the situation and ensure AFSPA is repealed. Tripura has done the right thing," CPI leader D Raja said.
A Hurriyat spokesman also said it is a bold decision.
"Many governments came and pledged to revoke AFSPA from the state but all these pledges and claims proved to be blatant lies made just for public consumption," he added.