Rozaliya Mukamazera, vice president of the National Electoral Commission (NEC) said the polls were generally peaceful, smooth, free and fair.
She said it was a smooth election with no irregularities reported and elections results were received electronically by the commission soon after tallying.
The Senate comprises of 26 members who serve for a five-year term that is renewable once.
These include 12 members who represent the country’s four provinces and the capital, Kigali, who are voted through electoral colleges.
The electorate is made up of members of district and sector councils.
Other Senate members include eight appointed by the Rwandan president, four elected by the Consultative Forum of Political Organisations, one representing public universities and higher learning institutions and another is elected to represent private universities.
During the election Monday, 12 senators were elected to represent the four provinces and Kigali.
Voting will continue today for one senator to represent public universities and higher learning institutions, and Wednesday elections will be conducted for the senator to represent private universities and higher learning institutions.
The final list of winners will be announced Sept 30, according to the National Electoral Commission.
A total of 63 candidates were nominated in August to campaign for the elections, according to the electoral commission.