The independent agency won the brief, from the Department for Business Innovation & Skills, after a pitch on 1 August against three agencies.
Engine’s role will be to design ads to inform the public about the Royal Mail IPO; although it has not yet been decided what form the campaign will take.
The Government confirmed in May that it intends to sell a majority stake in the Royal Mail through an IPO on the London Stock Exchange.
The sale is one of the largest privatisations in the UK for decades. It is expected to raise around £1 billion for the Government, valuing the organisation between £2 billion and £3 billion.
Julian Hough, a founding partner of Engine, said: "We’re delighted to have been appointed to this highly prestigious piece of business."