The renovation of the building is scheduled to take 52 weeks followed by 12-week fit-out, with a planned opening in autumn 2020.
Making the announcement, Council Co-Leader Councillor Douglas Lumsden said: "When completed, Provost Skene's House and the story of the City Region's enduring global influence will serve to inspire residents and visitors alike.
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"The £3.8 million we are spending on Provost Skene's House is part of an unprecedented capital investment programme being delivered by the Council."
Fellow Co-Leader Councillor Jenny Laing added: "This year will mark a step change in Aberdeen’s cultural, heritage and tourism offering.
"P&J Live and the redeveloped Aberdeen Art Gallery will open their doors and work will start on the transformation of Union Terrace Gardens."
PSH will showcase more than 100 individuals who helped shape the modern world through their endeavours in arts, science, business, sport and entertainment.
The Flourmill Lane building – which dates from 1545 – will include artefacts and memorabilia as well as bespoke audio-visual displays.
The Council's in-house building team will oversee delivery of the City Centre Masterplan project, which will including re-slating the roof and replacing rotten timbers.
The new attraction will be operated by the Aberdeen Art Gallery and Museums service.
(MH/JG)
