The South Andaman district administration confirmed 21 deaths and said 13 people were rescued.
The boat was travelling between Ross Island and North Bay, according to deputy commissioner of Nicobar P Jawahar.
The boat carrying 45 people - tourists from Kanchi Puram district of Tamil Nadu and Mumbai, and crew members -- sank on its way from Ross Island to North Bay.
The boat was called Aqua Marine and capsized between 3.45pm and 4pm.
The rescue operations are on. Civil administration and defence establishments like the Coast Guard conducted operations to rescue remaining passengers, the sources said.
Lt Governor Lt Gen (Retd) A K Singh announced an exgratia payment of Rs one lakh to the family of the deceased.
Singh also spoke to Union Home Minister Sushilkumar Shinde and briefed him about the rescue operations he ordered after the accident.
The rescued persons were admitted to G B Pant Hospital in Port Blair where the bodies were also taken for postmortem, the sources said.
The injured are being treated at GB Pant hospital. A magisterial enquiry has been ordered into the incident.
Though the boat had the capacity to carry only 25 passengers, it was overcrowded which led to the accident, the sources said.
A group of tourists from Kanchipuram district of Tamil Nadu who were staying in a resort at Prothrapur in South Andaman district, and another small group of tourists from Mumbai were on the boat, they said.
Helpline numbers set up at the district control room are: 1070, 03192-240127/230178/238881 and those in the G B Pant Hospital are: 03192-230629/9933274092. The local helpline number is 102.
Prime Minister Manmohan Singh has expressed shock over the accident. In an official statement issued by the Prime Minister's Office, Manmohan Singh "condoled the loss of lives".
The statement said the Aqua Marine, with 43 tourists onboard, capsized between Ross Island and North Bay near Port Blair, capital of the Andaman and Nicobar islands. "The prime minister has asked all central agencies to immediately assist in the rescue and relief operations," the statement said.