Election officials said Mr Kagame had 94% support with about half the districts reporting in Monday’s presidential vote, the first since a 1994 genocide that left some 800,000 people dead.
Most victims were minority Tutsis killed by Hutu extremists.
“This victory is a foundation for the next stage of development we are entering,” Mr Kagame told supporters. “Our victory should be a message to the outside world that Rwanda is on the right path.”
Monday’s election, the first in Rwanda in which there were opposing parties, was billed as a sign of how far the country has come since the 1994 slaughter.
Electoral Commission chairman Chrysologue Karangwa said Mr Kagame’s main competitor, Faustin Twagiramungu, had just 3.5% of votes reported, while the third candidate, Jean-Nepomuscene Nayinzira, had slightly more than 1%.
The election was “a sign that we are developing politically”, said Emmanuel Karisa, a 25-year-old university student.
“There was no choice in previous elections,” said 73-year-old Jean-Baptiste Gakwaya, referring to the two single-party Hutu regimes that had ruled Rwanda from the time it gained independence from Belgium in 1962 until the genocide.
After the election, Mr Kagame addressed thousands of backers and members of his Rwandan Patriotic Front gathering at Rwanda’s main Amahoro Stadium, where results were posted on the electronic scoreboard as they were read on radio and TV.
“I thank you for the confidence you have placed in me and I will not let you down,” said Mr Kagame, waving his baseball cap in salute to jubilant, dancing supporters.
Mr Kagame is a Tutsi who led the rebels who toppled the Hutu extremists in July 1994 to end the 100-day genocide. He then led the fight against remnants of the genocidal regime who attacked the country from bases in neighbouring Congo. The parliament elected him president in 2000.
More than 80% of Rwanda’s 3.9 million registered voters cast ballots at the 11,350 polling stations across the tiny central African nation of 8 million. Mr Kagame said the election results will show that Rwanda has made “huge strides” in building national unity and reconciliation.
Mr Twagiramungu, a Hutu, called the election “a very positive development and the ... basis for consolidating the democratic process in Rwanda”.