The PM has already reappointed Chancellor George Osborne, who has also been made first secretary of state.
Theresa May, Philip Hammond and Michael Fallon retain their jobs at the Home Office, Foreign Office and defence with other announcements due on Monday.
Mr 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 SNP 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 prime minister will spend the next 48 hours piecing together the new government.
George Osborne will act as Mr Cameron’s de facto deputy in the added role of first secretary of state.