Hundreds of his supporters took to the streets of the capital Monrovia, singing, dancing and embracing each other as news of his victory spread.
"I've never been so happy in all my life. We were in opposition for 12 years. We're going to make history, like the children of South Africa did," said Josephine Davies, vice president of the youth wing of Weah's Congress for Democratic Change.
French President Emmanuel Macron hailed the ex-star striker's victory in a tweet on Friday. "Congratulations to Mister George for this election! Great moment for Liberia!"
The NEC said Weah won 61.5% of the run-off vote, which was delayed several weeks after a legal challenge from Boakai, following October's first round.
It said that with 98.1% of all votes counted, Boakai had only secured 38.5% support.
Ahead of Thursday's result announcement, armed and helmeted police deployed outside the poll body's headquarters as Weah supporters gathered and began rejoicing.
Sirleaf's office said it had set up a team "for the proper management and orderly transfer of executive power from one democratically elected president to another", adding that it included several ministers.
Tumultuous history
The tumultuous events of the past 70 years in Liberia, where an estimated 250,000 people died during back-to-back civil wars between 1989-2003, have prevented a democratic handover from taking place since 1944.
Sirleaf's predecessor Charles Taylor fled the country in 2003, hoping to avoid prosecution for funding rebel groups in neighbouring Sierra Leone. Two presidents who served prior to Taylor were assassinated.
The UN and regional bloc ECOWAS hailed the peaceful nature of the vote, with UN Secretary-General Antonio Guterres praising "the government, political parties and the people of Liberia for the orderly poll", which the EU said "generally respected constitutional rules".
The Sirleaf administration, elected in 2005, guided the nation out of the ruins of war and through the horrors of the 2014-16 Ebola crisis, but is accused of failing to combat poverty and corruption.
Weah, the only African ever to have won both FIFA's World Player of the Year and the coveted Ballon D'Or, missed out on the presidency in a 2005 bid.
He was similarly frustrated when he ran for vice-president in 2011, but his CDC party repeatedly urged its young and exuberant supporters to keep calm.
Weah's latest campaign was not without controversy, however.
He has drawn some criticism for picking Jewel Howard-Taylor, the powerful ex-wife of Charles Taylor, as his vice-president.