One small aircraft slammed into the main government tax office in central Colombo late on Friday, killing at least two people and wounding 53, the military said.
The other was shot down and crashed in a marsh outside the international airport, the site of the Tiger air wing's first strike in 2007. The attack had set off volleys of anti-aircraft fire across Colombo.
Authorities said the two planes were the last aircraft at the disposal of the Liberation Tigers of Tamil Eelam
"It is a great victory in the fight against terrorism that we were able to bring down the two aircraft," Defence Spokesman and government minister Keheliya Rambukwella said.
Minister Rambukwella said the rebels' air force, the only air unit of a terrorist outfit in the world, had been a threat to the entire region. Neighbouring India has nuclear facilities in its southern states.
The attack was proof of the Tigers' ability to strike far from the war zone, where troops have rapidly encircled them in just 73 sq km (28 sq miles) of jungle and are within reach of ending a separatist war that began in 1983.
In a news release on Saturday, the rebels said the raid targeted Sri Lanka's air force headquarters in Colombo and airbase at the international airport, pro-rebel web site www.TamilNet.com reported.
TamilNet said the mission was flown by "Black Air Tigers", or suicide pilots. Both planes came close to their targets. The tax office is near the air force headquarters and the crash site of the second plane was adjacent to the boundary of the airbase.
The Tigers' ramshackle air squadron had flown nine previous sorties since debuting in 2007. The military said it shot down one plane in September, but no wreckage was found.
The LTTE is on the verge of defeat with more than 50,000 soldiers surrounding them in the northern war zone. The military said heavy fighting was ongoing.
Tens of thousands of civilians are trapped in the war zone, many of them forcibly kept there by the LTTE and others fearing heavy shelling, according to people who have escaped.