Speaking at the service in Honiara, Prime Minister Manasseh Sogavare said the twin disaster was the worst incident in the country's history since World War II.
More than 6,000 people lost their homes in western provinces of the Pacific state, and three weeks on, many villagers are still living in makeshift camps on higher ground, too frightened to return home.
Mr Sogavare, who has visited the affected areas, told mourners he had witnessed first-hand the destruction wrought by the earthquake and the tsunami that followed it.
"I was encouraged by the determination of the people to rebuild their lives," he said.
Mr Sogavare praised the relief effort and the work of people who have risked their lives to save others.
"At Titiania village a six-year-old lost his own life trying to save the life of his three-year-old sister. It was a willing act of sacrifice," he said.
A minute of silence was observed at 7.39am local time across the Solomons, marking the moment when the 8.0 magnitude earthquake struck three weeks ago.
Today has been declared a national day of mourning, and shops and businesses across the Solomons are closed.
Another memorial service was held on Gizo, the island worst affected in the disaster.
The National Disaster Management Office says the focus of the relief operation is now on long-term rehabilitation of affected areas.
AFP reports that the government plans to relocate low-lying communities to higher ground to keep them out of the path of any future tsunamis.