Ordering the grey-haired Mladic to stand for the final part of the ruling, chief judge Prisca Nyambe said the appeals chamber of five judges "dismisses Mladic's appeal in its entirety".
Nyambe, who dissented to the findings of all the other judges, added that the court "affirms... the sentence of life imprisonment imposed on Mladic by the trial chamber."
The court also dismissed a prosecution appeal against Mladic's acquittal on wider genocide charges.
Mladic, who gives his age as 78 but it is 79 according to the court, is currently being held in the Netherlands but will serve the rest of his sentence in a yet-to-be-decided country.
Relatives of some of the Srebrenica victims were outside court for the verdict.
"Today is a historic day, not only for us mothers, but also for the whole Balkans, Europe and the world," Munira Subasic, president of one of the "Mothers of Srebrenica" associations, told AFP outside court.
"He's a monster who did not repent for what he has done, even after 26 years. Wherever their army came, wherever their boot stepped in, they committed genocide," she added.
Mladic was the military face of a brutal trio led on the political side by ex-Yugoslav president Slobodan Milosevic and former Bosnian Serb leader Radovan Karadzic as the former Yugoslavia descended into carnage after the fall of communism.
Karadzic is currently serving a life sentence while Milosevic died in The Hague in 2006.
At the genocide memorial near Srebrenica, a giant screen broadcast witness testimony ahead of the verdict, near the lines of white headstones where the bodies of some 6,600 identified victims were laid to rest.
"Instead of rejoicing with grandchildren, I have come to cry here," said Munevera Kabeljic, 69, resting on the graves of her husband and her sons aged 17 and 20, neither of whom were married.
Kabeljic hit out at members of the Serbian community in Bosnia who have denied that any massacre took place. "What hurts the most is that they deny genocide," she added.
"They say it didn't happen, but these tombstones prove it. They didn't come to sleep here, they were killed."
'Prevent future atrocities'
The verdict was hailed as a victory for international justice in an age of increasing impunity.
"This historic judgment shows that those who commit horrific crimes will be held accountable," Biden said in a statement. "It also reinforces our shared resolve to prevent future atrocities from occurring anywhere in the world."
UN rights chief Michelle Bachelet said the ruling "highlights the determination of the international justice system to ensure accountability no matter how long it may take -- in Mladic's case, nearly three decades after he committed his appalling crimes."
Captured in 2011 after a decade on the run, Mladic was found guilty in 2017 of genocide for personally overseeing the massacre.
Footage from the time showed him handing out sweets to children before they and the women of Srebrenica were taken away by bus, while the men of the town were marched into a forest and executed.
Mladic was also found guilty of orchestrating a wider campaign of "ethnic cleansing" to drive Muslims and Bosnians out of key areas to create a Greater Serbia. The war left around 100,000 people dead and 2.2 million displaced.
Mladic insisted throughout the trial and appeal process that he was not guilty of genocide or war crimes. In one of a series of tirades to the court, he painted himself last August as a "target of the NATO alliance" and derided the court as a "child of western powers".
His lawyers argued he was far from the scene at the time of the killings in Srebrenica and that he could not be held responsible for the crimes of his subordinates.
The appeal hearing was delayed repeatedly after Mladic needed surgery to remove a polyp and then because of the Covid-19 pandemic. Access to the court on Tuesday was also limited because of coronavirus measures.