Some of the key posts will carry on with business as usual including Chancellor George Osborne, Home Secretary Theresa May, Foreign Secretary Philip Hammond and Defence Secretary Michael Fallon while other announcements are due on Monday.
Osborne, Cameron's neighbour at No 11 Downing Street, has also earned an honorific title of first secretary of state, which formally indicates his seniority over other ministers.
Indian-origin MPs Priti Patel and first-timer Rishi Sunak are expected to get a nod within some of the new appointments.
Early speculation over changes at the top of the new ministerial ladder in Britain include rumours that Iain Duncan Smith, the work and pensions secretary in the coalition government, would be replaced by Sajid Javid, the culture secretary.
The maximum number of paid government appointments is fixed by law at 109.
Although some will be filled by peers, it means that Cameron can rely on support from one in three of his MPs in all divisions.
The newly-elected PM will spend the weekend finalising who will join him at the top table to replace Lib Dems who held cabinet posts in the coalition government such as former Business Secretary Vince Cable, Energy Secretary Ed Davey and Chief Secretary to the Treasury Danny Alexander.
He will also consider whether to find a role for Boris Johnson, who was elected to Parliament on Friday after a seven-year absence from the House of Commons.
Johnson has a year left to serve as mayor of London and has indicated that he may not take on a ministerial role over and above his mayoral one.
Cameron, who has promised to lead a government for "one nation" after his party won its first majority since 1992 with 331 seats, has already spoken to SNP leader Nicola Sturgeon, whose party won 56 of the 59 seats in Scotland.
The Scottish National Party, who made history with their best electoral performance, is expected to press for more devolved powers for the Scottish Parliament, going beyond what was proposed by the Smith Commission after last year's independence referendum.
The Conservatives have said they will seek to deliver all of their election manifesto in government, focusing on tax cuts, extending access to childcare, extending home ownership and giving the public a say on the UK's future membership of the EU.
The party has also promised an in-out referendum on the UK's future in Europe to be held in 2017.
Meanwhile, Opposition Labour and the Lib Dems are beginning the search for new leaders.
Ed Miliband and Nick Clegg both resigned on Friday, as did UKIP leader Nigel Farage, after election disappointments, leaving their parties to consider who is best placed to lead opposition to the new government.