In the new role, Oliver will team up with Michael Portillo's former press secretary Malcolm Gooderham, who is MD of the independent agency.
The lobby journalist will start later this month, as party conference season gets under way.
Oliver's departure from The Sunday Times was reported by prweek.com on 29 July, but his next move has been a closely guarded secret.
His capture by TLG signals the latest stage of an aggressive expansion by the agency, which was set up in late 2007 and now has 12 full-time staff.
Earlier this year, TLG snared McDonald's top UK lobbyist Hugh Milward.
Gooderham said he had ambitious plans to keep expanding the agency. 'We're increasing our investment in new ideas and people as it is the combination of both that distinguish the most successful businesses,' he said.
Oliver told PRWeek that corporate PR could benefit from more journalistic know-how. 'In my experience,' he said, 'I'm surprised by how minor incidents in corporate and political life turn into major crises due to misjudging public mood and how best to engage with the media online and in the traditional media.'
Oliver joined The Sunday Times at the end of 2007, having previously been deputy political editor of the Mail on Sunday. He is the latest in a long line of senior journalists to move into PR in recent years.
Also making the move from journalism to PR this week is senior Sun political journalist Katherine Bergen. She joins strategic comms agency Gardant, having previously been editor of The Whip column.
Hack to flack
August 2010: Stefan Stern, who wrote management columns for the FT, joins Edelman as strategy director.
February 2010: Edelman hires BBC's director of global news Richard Sambrook as global vice-chairman.
November 2009: The Sun's political editor George Pascoe-Watson joins Portland as a partner.
December 2009: Sunday Times business editor John Waples named MD at financial PR firm FD.