Guru was hanged in jail no 3 in Delhi Tihar Jail.
Union Home Minister Sushilkumar Shinde said Afzal Guru confirmed that Guru was hanged at 8 am.
Fearing backlash, curfew has been imposed in all major towns in the Kashmir Valley. Chief Minister Omar Abdullah is closely monitoring the situation.
Union Home Secretary R K Singh said Home minister recommended Guru's hanging on January 23 and the President rejected the mercy plea on January 26.
Guru was convicted of conspiracy in the December 2001 attack on Parliament and was sentenced to death by the Supreme Court in 2004.
On December 13, 2001, five heavily-armed gunmen stormed the Parliament complex and opened indiscriminate fire, killing nine persons. They included five Delhi Police personnel, a woman Central Reserve Police Force (CRPF) official, two Parliament watch and ward staff and a gardener.
A journalist, who was injured, died later. All five terrorists were shot dead.
A year later, four accused, including Afzal Guru, were arrested for the attack and found guilty after a trial.