The bridges had been swamped by water due to heavy rains, that turned some parts of the state into lakes.
Local television coverage showed one bus upended in a fast-flowing river.
A police spokesman at the scene of one of the accidents near the town of Pattukottai in remote Thanjavur district said at least 49 people died when a bus plunged into a canal.
"Of the 49 bodies recovered there are two bodies which are not identified. The rest have been handed over to the relatives," the spokesman said.
"Bodies are being recovered as far as 15km from the spot where the bus was washed away," he said.
Police and fire rescue teams were searching the site for more bodies from the accident.
Workers also rescued 36 people who are being treated for injuries, district official M Veerashanmughamonie said.
The second bus was washed away by flood waters from the swollen Sirugani river in the Ramanathapuram district.
A report from the Press Trust of India news agency there said at least 50 people drowned.
About 27 bodies have been recovered while 30 people were rescued, said K Sellamuthu, a local administrator.
"We are still looking for the bodies downstream, but are also enquiring locally whether any of them survived"
Six passengers are still unaccounted for, Sellamuthu said.
"We are still looking for the bodies downstream, but are also enquiring locally whether any of them survived," he said.
The bus driver and the conductor survived but the police have arrested the pair for defying an order banning anyone from crossing the bridge, Sellamuthu said.
The passengers were travelling to a temple town, the report said, adding the river was high due to unseasonal persistent rain falling on parts of coastal Tamil Nadu.
The storms, caused by low pressure in the Bay of Bengal, have been battering Tamil Nadu for several days, causing road and rail chaos and widespread flooding in many parts of the state.
Hundreds of thousands of people have been forced from their homes in coastal districts.
Rescuers waded through muddy water up to their necks, pushing people who could not walk in black tyre tubes.
A coastguard helicopter was dropping food packets to marooned villagers, a district official said.