In a statement, former President Barack Obama said Annan embodied the U.N.'s mission like few others.
The Elders organisation - a group of statesmen co-founded by Annan which speaks out on global issues - hailed the former United Nations chief as "a voice of great authority and wisdom in public and private".
After his death, tributes have been paid from across the world to the former United Nations chief.
His foundation described Mr Annan as a "deeply committed internationalist" who worked "tirelessly" for the cause of peace.
Mr Guterres led the tributes to his predecessor.
Cuban President Fidel Castro (left) and Secretary-General of the United Nations Kofi Annan review a guard of honour upon Annan's arrival in Havana on April 11, 2000.
Kofi was the epitome of human decency and grace.
Russian President Vladimir Putin hailed his "wisdom and courage", while German Chancellor Angela Merkel celebrated the "exceptional statesman in the service of the global community".
Despite the lows, he left the post as one of the most popular United Nations leaders ever, and was considered a "diplomatic rock star" in worldwide diplomatic circles. A year later he established the Kofi Annan Foundation in the Swiss city. He was a citizen of the world.More news: Paul Finebaum Thinks Urban Meyer Survives at Ohio State
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UK PM Theresa May and North Atlantic Treaty Organisation chief Jens Stoltenberg were also among those who paid tributes.
In a telephone call to President Nana Akufo-Addo of Ghana on Saturday from London, President Buhari commiserated with the government and people of the country on the passing of the diplomat.
The Ghanaian continued to champion the protection of gay people after his tenure as the world's top diplomat had ended.
Kofi Annan described his greatest achievement as the Millennium Development Goals which - for the first time - set global targets on issues such as poverty and child mortality. The drive is widely regarded as a success.
Even out of office, Mr Annan never completely left the United Nations orbit. As the head of peacekeeping operations starting in 1993, Annan would "be sorely tested by devastating wars in Somalia, Rwanda and Bosnia", NPR noted in 2012.
He resigned later that year, frustrated over the lack of progress in ending the violence.
"The U.N. can be improved, it is not flawless but if it didn't exist you would have to create it", he told the BBC's Hard Talk during an interview for his 80th birthday last April, recorded at the Geneva Graduate Institute where he had studied.
"The world has lost a great humanitarian, leader, and self proclaimed "stubborn optimist".
He headed his own foundation and was chair of The Elders, which had been founded by the late South African president, Nelson Mandela. He was once quoted as saying, "I walked away as a young man convinced that change is possible, even radical revolutionary change".