Chidambaram's son Karti heaved a sigh of relief, tweeting, "Phew. At last after 106 days."
Scores of Congress workers and supporters greeted Chidambaram as soon as he stepped out of the Tihar jail and gave a rapturous welcome.
"After 106 days of pre-trial incarceration, not a single charge has been framed against me," Chidambaram told reporters outside the prison and then went on to meet party president Sonia Gandhi, who has extended her complete backing.
Speaking to reporters after meeting Sonia Gandhi, Chidambaram said, "I am happy that the Supreme Court has passed an order granting bail and I am happy that I have stepped out and breathing the air of freedom after 106 days."
He said he will address a press conference on Thursday.
Earlier, Congress leader Adhir Ranjan Chowdhury accused the government of hatching a "big conspiracy" against Chidambaram and said walls were scaled to arrest him as if it was the house of "Osama bin Laden's relative" and not of a former Union minister.
"On the orders of this government, walls were scaled of the home of Chidambaram, a former home minister and finance minister, to arrest him as if a relative of Osama bin Laden was staying there. Such behaviour meted out to him is not appropriate," he said.
Asked if Chidambaram was treated like a terrorist, Chowdhury said, "That is what it looks like."
He said the action against Chidambaram was "vendetta politics" which was "harmful for our democracy".
As the news of the Supreme Court granting bail to Chidambaram broke out, several party leaders expressed solidarity with Chidambaram and accused the government of playing "vendetta politics".
Chidambaram's lawyer and party colleague Abhishek Singhvi described the ruling as an "excellent light after a rather long tunnel".
"Truth finally prevails #SatyamevaJayate," tweeted the Congress from its official handle.
Senior Congress leader Shashi Tharoor was more circumspect and said "justice delayed is justice denied", adding the bail should have been granted much earlier.
A three-judge bench, headed by Justice R Banumathi, granted bail to the 74-year-old former Union finance minister, who has been in custody since August 21 when he was arrested by the CBI in the INX-Media corruption case. The Enforcement Directorate had arrested him on October 16 in the money laundering case.
Singhvi termed the order "balanced", "nuanced" and "comprehensive", and a great order in favour of human rights and balanced jurisprudence.
The BJP took a dig at the Congress's reaction following the Supreme Court bail, saying that Chidambaram has joined the "Out On Bail Club".
Asked about the BJP's allegations against his father, Karti told a TV channel, "If they have evidence, they must take it to the court and put it before us and not hide behind this sealed cover tactic... Nobody is saying we won't face trial. I'm happy to face trial."
He also said Chidambaram will be in Parliament on Thursday at 11 AM.
Rajasthan Chief Minister and senior Congress leader Ashok Gehlot echoed the party to say truth had prevailed.
Deputy leader of opposition in Rajya Sabha Anand Sharma said quest for truth has been vindicated and justice has finally prevailed.
"Clearly, he (Chidambaram) is a victim of vendetta politics which remains a threat to our Constitutional democracy," Sharma said in a tweet.
Senior Congress leader Milind Deora said imprisoning an accused for 106 days is a "travesty of justice".
"We must not forget that bail is the rule & jail is the exception. I look forward to P Chidambaram ji's much-needed suggestions for tackling India's economic slowdown," he tweeted.
Party leader Ahmed Patel met Chidambaram at his residence.
The top court said Chidambaram can't leave the country without prior permission of the court and should neither try to influence the witnesses nor tamper with evidence.
The apex court set aside the Delhi High Court's November 15 verdict denying bail to him.