Gibb entered Downing Street as director of communications in 2017, replacing Katie Perrior, who resigned following May's calling of the general election that year.
He was among May's closest advisers, advising on Brexit alongside policy areas including the NHS and plastic waste reduction.
Gibb was previously head of BBC Westminster, with overall responsibility for its political output including the Daily and Sunday Politics, The Andrew Marr Show, This Week and Radio 4’s Westminster Hour. He also helped steer the BBC's EU referendum coverage.
Kekst CNC said Gibb's role at the agency will be to "provide counsel to boards and management teams both in the UK and internationally across a range of business-critical issues".
Kekst CNC partner Richard Campbell said: "Robbie is a seasoned political adviser, broadcast journalist and communications professional with a strong knowledge of the British political landscape and an expert understanding of the Brexit process.
"At this time of political and corporate uncertainty, his recommendations and insight will be invaluable to our clients around the world. We are delighted he is joining Kekst CNC, complementing the skills and expertise of our growing team."
Gibb recieved a knighthood for "political and public service" in May's Resignation Honours, which also saw the former Prime Minister's ex-spokesman James Slack receive a CBE for "public service".
Gibb's successor at Downing Street under Boris Johnson is former Mirror journalist Lee Cain.
Kekst CNC, which formed one year ago with the merger of Publicis agencies Kekst and CNC, has a 300-strong workforce across 13 offices in the US, Europe, the Middle East and Asia.
In July, the agency topped the Mergermarket table ranking PR agencies by the number of M&A deals they handled globally in the first half of 2019, with 124.
New additions at the London office include former Brunswick director Joe Shipley, who was hired to spearhead the public affairs arm. In the summer it was reported that Kekst CNC is providing corporate communications support to Saudi Aramco as the oil company was said to have restarted work toward an initial public offering.