0600 GMT March 18, 2019
The commission said that partial results of Friday's election had given him 98 percent of the votes, BBC reported.
Kagame's supporters began celebrating before the announcement.
They say that he has brought stability and economic development after the horrors of the 1994 genocide.
But his critics — most of whom are outside the country ― say he has ruled through fear.
Kagame, who has been in power for 17 years, was challenged by Frank Habineza and Philippe Mpayimana.
He came to power in 1994, when his rebel group took control of the capital, Kigali, ending the genocide in which some 800,000 ethnic Tutsis and moderate Hutus were slaughtered.
Rwanda's constitution was amended in 2015, giving Kagame a chance to stay in power until 2034.
The two challengers have complained that their supporters are being intimidated, which they say explains the low turnout at their pre-election rallies.
The candidates have also accused some local authorities of undermining their campaign.