The actor and producer, who is married to Emma Thompson, has starred in the likes of The Crown (as Lord Mountbatten), Sense and Sensibility and Cranford.
In a statement, Greg explained his inspiration behind agreeing to Strictly this year.
"My beautiful sister was a huge disco queen. She left our world almost exactly five years ago in a glitter ball coffin. This is for her. My gorgeous Diva sis, who would have been insane with excitement that her little bro was doing this.
"I will channel her, as her bro can’t dance – but I’m thrilled to be dipping my toes, knees, hips and arms into this wonderful world, and hope to make her proud, and obviously make her laugh." he added.
Greg met Oscar-winner Emma on the set of Sense and Sensibility (1995) and they married in 2003.
They are parents to daughter Gaia and adopted son Tindyebwa Agaba.
Greg wrote Paul Fieg's festive movie Last Christmas, in which Emma also starred.
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Greg was revealed as the latest star to sign up for the BBC dance show on This Morning today (11th August), shortly after hosts Eamonn Holmes and Ruth Langsford announced Tilly Ramsay was the ninth contestant for Strictly Come Dancing 2021.
Strictly Come Dancing 2021 will launch later this summer on BBC One. If you're looking for more to watch, check out our TV Guide. Visit our Entertainment hub for all the latest news and Strictly announcements.