"For the last 30 years, our country has been good work in progress. This new mandate means the beginning of even more hard work," Kagame said.
"That expectation to keep improving is not a dream, it is a reality. We can do it and we will do it.”
Sunday's swearing-in took place at Kigali's Amahoro national Stadium, with thousands in attendance, many wearing T-shirts in the yellow, green and blue colours of the national flag.
Kagame received a military 21-gun salute, accompanied by cheers from the crowd. Twenty-two heads of state from African countries were in attendance.
Rwanda's constitution was changed in 2015, allowing Kagame to extend his time in office.
The two men who vied against him last month - Frank Habineza from the Democratic Green Party and independent Philippe Mpayimana - both conceded defeat in the election, which rights groups say was marred by a crackdown on media, the opposition and civil society groups.
A government spokesperson repeatedly rejected such criticism during the election period.
Source: Reuters