Sri Lankan military officials and hospital sources said that the soldiers were travelling to join the fighting when their bus was hit by a Claymore mine on Monday evening.
"They did not expect a Claymore mine attack at that time of the night because usually troops travel on the main road during the day," a local military official said.
Officials said 10 soldiers had died instantly and nine others were declared dead on admission to a local hospital.
Two soldiers who survived the blast were air-lifted to a larger hospital in the region.
Earlier on Monday, Tamil Tiger rebels said that Sri Lanka's four-year ceasefire was over and the island's two-decade civil war back on.
"The war is on and we are ready," S. Elilan, the head of the Tigers' political wing in the restive eastern district of Trincomalee, said on Monday.
"The war has begun. It is the government which has started the war... The ceasefire agreement has become null and void."
On the ground, Tamil rebels fired artillery at troops in northern Sri Lanka on Monday, opening a new front in clashes as the army pushed toward rebel territory in the northeast, the military said.
Elilan confirmed the fighting, saying the government forces were continuing an advance towards their forward defence line in the east in a water supply dispute.
He said, "Militarily we have decided to fight back if the Sri Lankan army enters our area."
The independent Daily Mirror quoted the rebels as saying on Monday that the government offensive in northeastern Trincomalee had forced 3,000 Tamil residents to flee the area.
Military officials also said that 35 Tamil Tiger fighters were killed in the fierce fighting over a waterway in the north-eastern Trincomalee district on Monday.
The pro-Tigers Tamilnet.com website said the Tigers resisted the military advance and did not mention any casualties.
"The Sri Lanka army began moving ground troops from two bases towards Maavilaru sluice gate Monday morning," the website said. "The Sri Lanka army troops were defeated by the Tigers."
The military said the Tigers opened fire at troops in Nagarkovil, which falls on the front lines between rebel and government held areas in the northern peninsula of Jaffna, causing no casualties.
"The ceasefire agreement has become null and void at the moment"
S. Elilan, the head of the Tigers' political wing in the restive eastern district of Trincomalee
Brigadier Prasad Samarasinghe, the military spokesman, said: "The terrorists fired at our troops in Nagarkovil in Jaffna and we retaliated."
Separately, Samarasinghe said government troops were making little progress in trying to reach a site where the guerrillas were blocking the flow of water from a plant to villages in government-held territory.
Keheliya Rambukwella, the chief government spokesman, said the troops were hampered by landmines and because the insurgents had positioned themselves on high ground.
On Sunday, air force planes bombed rebel positions in the area of the water blockade after government troops came under rebel mortar fire, Rambukwella said.
Under the terms of the cease-fire, the government and rebels must seek permission before entering each other's areas.
Months of violence, including clashes between government forces and the rebels, have killed about 800 people and battered the fragile 2002 cease-fire, which was meant to end two decades of fighting that claimed the lives of about 65,000 people.