Former journalist Oliver arrived at Number 10 with no prior PR experience, but was seen as a strong performer in the role.
He also avoided the controversy that plagued his predeccessor, former News of the World editor Andy Coulson, who had resigned over the phone-hacking scandal for which he would later serve five months of an 18-month jail sentence.
He will join Teneo Blue Rubicon - the business created after Blue Rubicon was acquired by US firm Teneo last year, and rebranded in September - in December.
The agency declined to comment on likely clients or duties for Oliver, who will sit as one of the firm's most senior employees under Charles Watson, the chair of Teneo International, and CEO Gordon Tempest-Hay.
In recent weeks Teneo Blue Rubicon has won a string of sizeable accounts, including the global corporate comms brief for Diageo, and Halfords' financial brief. Earlier this year it was appointed to a major turnaround brief with the bank RBS, and ongoing clients include McDonald's and Tesco.
Oliver's appointment had been rumoured earlier in October - this is understood to be the result of the leak of information from his application to the Advisory Committee on Business Appointments, asking for permission to take on the role.
PRWeek understands that permission has been granted. However, ACOBA letters of approval are normally published one or two months after being sent to individuals.
The letter will set out, as per rules on business appointments, that Oliver should not use privileged information available to him from his time at Number 10, and should not be personally involved in lobbying the UK Government for two years from when he left Downing Street.
Since leaving Downing Street, Oliver has written the book Unleashing Demons: The Inside Story of Brexit.