Robinson was ITV's political editor and he beat a number of other candidates for the top job.
The race for Marr's replacement started on May 13 when he resigned as political editor to replace Sir David Frost as presenter of the BBC's new Sunday morning political show.
Robinson, 'Newsnight' political editor Martha Kearney and BBC economics editor Evan Davis were all considered frontrunners for the job.
Robinson was appointed political editor for ITV News in 2002 following his role as chief political correspondent for BBC News 24.
Before joining News 24, Oxford-educated Robinson was the presenter of 'Late Night Live' and 'Weekend Breakfast' on BBC Radio Five Live.
He has also held posts as deputy editor of 'Panorama' and 'On the Record' on the BBC.
Mark Byford, BBC deputy director-general, said Robinson was the right man to succeed Marr.
"Nick's passion, energy, insight and political knowledge are matched by his outstanding communication skills and deep commitment to fairness and impartiality," he said.
Marr had been political editor at the BBC since May 2000. He also presents 'Start the Week' on Radio 4 and other current affairs TV and radio including BBC One's 'Panorama' political strands.
The new as-yet-to-be-named series, with Marr at the helm, will broadcast in the same slot as 'Breakfast with Frost' from September.
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