Blackhurst, whose contract with Independent and Standard owner ESI Media has now come to an end, will join Crosby Textor in March in "a senior executive role".
Blackhurst told PRWeek that he would be providing "strategic advice to both political and corporate clients".
Crosby Textor describes its work as "research, strategies, results" but does not divulge its clients. It is headquartered in London, with eight staff there and another 20 in offices around the world.
Australian Crosby was knighted in the most recent New Year's Honours list after masterminding the Conservatives' comprehensive victory in the 2015 general election. Crosby has helped win several general elections in Australia for centre-right parties and advised Boris Johnson on both his London mayoral victories. He is now a UK resident.
Blackhurst, 56, became editor of The Independent in 2011, having been City editor of several newspapers including a long stint at the London Evening Standard. He was vocal in leading the newspaper industry's response to the Leveson Report in 2012.
After Amol Rajan was appointed editor of The Independent in 2013, Blackhurst remained an employee of ESI, first as group head of content and then as a features and opinion writer.
Cambridge-educated Blackhurst is the son of a Conservative councillor from Barrow-in-Furness. He is renowned as well networked in the corporate world with close relationships to powerful City PRs such as Roland Rudd and Sir Alan Parker.
In 2011, on the occasion of the paper's 25th anniversary, newly appointed Blackhurst told PRWeek sister title MediaWeek he doubted the Independent would be around to celebrate its 50th anniversary, saying: "If the industry was staying the same, yes. But can I see any paper lasting for 25 years? I really don't know."