Morgan, who also penned Frost/Nixon, The Last King Of Scotland and Rush, will be honoured at the annual BFI Chairman's Dinner later this month.
He said he could not be more “surprised, thrilled or proud” to receive the honour, adding he would “look forward to being suitably teased and abused on the night”.
Josh Berger, chairman of the BFI, will host the dinner at Claridge's in London on February 21 and said: “I am absolutely thrilled to be recognising Peter Morgan's rare talent and enormous contribution to both the big and small screen with a BFI Fellowship.
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Peter Morgan will be awarded with the British Film Institute Fellowship award
I am absolutely thrilled to be recognising Peter Morgan's rare talent and enormous contribution to both the big and small screen with a BFI Fellowship
Josh Berger, BFI chairman
“He is rightly one of our most feted and accomplished screenwriters, with a career spanning almost 30 years and delighting generations of audiences with his work.
“Peter has an uncanny knack for getting under the skin of prominent figures to portray an eclectic range of real-life personalities, retelling the most iconic moments in our recent history and the individuals at the heart of them, to make engaging, elegant and accessible stories.”
Much of Morgan's work has focused on the British establishment and real-life characters and he is responsible for a trio of films that starred Michael Sheen as Prime Minister Tony Blair: The Deal, The Queen and The Special Relationship.
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Morgan has a career spanning almost 30 years
He will join a respected list of fellows including Tim Burton, Clint Eastwood and Dame Judi Dench but will be one of the first known principally for his writing.
The only other recipients honoured primarily for their writing are Graham Greene and Lynda La Plante.