Nineteen African heads of state were present at the ceremony which took place in front of a packed crowd in the national stadium in Kigali, entertained by a military parade and drummers.
The 59-year-old Kagame, who was re-elected with nearly 99 per cent of the vote, took a swipe at critics who regularly highlight repression and lack of freedoms in the tiny east African nation.
"Every African country has to contend with efforts to force us to live on someone else's terms," he said.
Among those attending the ceremony was Sudanese President Omar El Bashir, who is wanted by the International Criminal Court for genocide crimes committed against humanity.
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Rwanda is however not a signatory to the ICC and is not obliged to enforce Bashir's arrest.
Notable absentees included Burundi's Pierre Nkurunziza and Joseph Kabila of the Democratic Republic of Congo (DRC), who have endured a frosty relationship with Kagame -- who appeared to reach out to his adversaries both at home and abroad.
Kagame won the August 4 election with 98.79 percent of votes against two little-known candidates.
Human Rights Watch (HRW) said in a statement Friday the victory followed a campaign in which Rwandans were forced to donate money to the ruling party and blocked from attending opposition rallies.
"Kagame's landslide win came as no surprise in a context in which Rwandans who have dared raise their voices or challenge the status quo have been arrested, forcibly disappeared, or killed, independent media have been muzzled, and intimidation has silenced groups working on civil rights or free speech," said Ida Sawyer, HRW's Central Africa director.
"It was easy to see who I was voting for on the ballot, so it was impossible for me to vote for anyone besides Kagame," he was quoted as saying.
After the election, the United States said it was "disturbed by irregularities" observed during voting.
Kagame has ruled Rwanda with an iron fist since 2000 and will now be president until 2024, at which time he could seek two extra five year terms after a 2015 constitutional amendment.
He is credited with stabilising Rwanda after some 800,000 people -- mainly minority Tutsis -- were killed in the 1994 genocide at the hands of extremist Hutus.
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