Scott, a Cambridge-educated economist born to Scottish parents, was Sata's vice president. He takes over as interim leader until an election in three months, making him the first white African leader since South Africa's F.W. de Klerk lost to Nelson Mandela in the 1994 election that ended apartheid.
"Elections for the office of president will take place within 90 days. In the interim I am acting president," Scott said in a brief televised address.
(READ MORE: Guy Scott could be Africa’s only white president, just for 90 days)
"The period of national mourning will start today. We will miss our beloved president and comrade."
Scott, 70, will not be eligible to run for the presidency because of citizenship restrictions, analysts say.
Sata, an abrasive figure nicknamed "King Cobra" because of his venomous tongue, died on Tuesday in London, where he was receiving medical treatment, the government said earlier. He had been president of Zambia, Africa's second-largest copper producer since 2011.
The cause of death was not immediately disclosed, but Sata had been ill for some time. He was being treated at London's King Edward VII hospital when he died, the website Zambian Watchdog reported.
(READ MORE: Zambian president Sata dies in London aged 77)
"As you are aware, the president was receiving medical attention in London," cabinet secretary Roland Msiska announced on state television. "The head of state passed away on October 28. President Sata's demise is deeply regretted."
Sata, whose populist platform included defending workers' rights, was often fiercely critical of the foreign mining companies operating in Zambia's copper belt. Analysts said his death could prompt a rise in investment in the country.
"President Sata has been a divisive figure for Zambia on the economic front, espousing increasingly authoritarian and ad hoc policy measures against the crucial mining sector in recent years, which has hampered investment," South African consultancy ETM said.
"The president's passing could make way for a more reformist administration and help to remove broader policy uncertainties."
Sata, whose varied CV included stints as a policeman, car assembly worker, trade unionist and platform sweeper at London's Victoria station, left Zambia on Oct. 19 for medical treatment, accompanied by his wife and family members.
Defence Minister Edgar Lungu, secretary general of Sata's Patriotic Front party, had to lead celebrations last week of the 50th anniversary of Zambia's independence from Britain.
Concern over Sata's health had been mounting since June, when he disappeared from the public eye without explanation and was then reported to be receiving medical treatment in Israel.
He missed a scheduled speech at the U.N. General Assembly in September amid reports that he had fallen ill in his New York hotel. A few days before that, he had attended the opening of parliament in Lusaka, joking: "I am not dead."
It was a typically no-nonsense denial from a politician not known for diplomatic niceties.
"I haven't bloody lost so don't waste my time," he barked at a BBC reporter in 2008 after results showed he had indeed lost an election to his main rival, Rupiah Banda, albeit by the narrowest of margins.
Although he toned down the nationalist, anti-Chinese rhetoric that finally helped him oust Banda in a 2011 election, he would still deliver occasional rants at the foreign miners.
(READ MORE: Government guarantees a concern for Zambian mining companies)
A year ago, he threatened to remove the mining licence of Konkola Copper mines, Zambia's biggest private employer, because of plans to lay off 1,500 workers. During the row, the company's foreign chief executive had his work permit revoked.
The Zambian kwacha fell 2 percent against the dollar after Sata's death was announced. Traders said it was unlikely to suffer any prolonged weakness because of the underlying health of an economy expected to grow 7 percent this year.
"Obviously, there will be a sentimental temptation to go long on dollars, but I'm also quite confident the central bank will do everything it can to protect the currency," one Lusaka-based trader said.
"In terms of the economy, everything should still be on track."