The "James Bond" star will play Norman Scott, the former lover of disgraced politician Jeremy Thorpe (Grant) in the real-life story, based on the book by John Preston, reported Deadline.
Stephen Frears is directing "A Very English Scandal", being written by Russell T Davies. Executive producers are Dominic Treadwell-Collins, Graham Broadbent and Pete Czernin for Blueprint Television and Lucy Richer for the BBC, with Dan Winch producing.
"It's a dream come true, to work with Ben. One of Britain's finest actors playing one of history's most fascinating men," said Davies.