The star's acclaimed movie about the real-life 1979 Iranian hostage crisis beat out the likes of Les Miserables, Life Of Pi, Lincoln and Zero Dark Thirty for the ceremony's main prize.
He was also named Best Director, ahead of Oscar nominees Michael Haneke (Amour) and Ang Lee (Life Of Pi) and Quentin Tarantino (Django Unchained) and Kathryn Bigelow (Zero Dark Thirty), who, like him, were snubbed by Academy Awards voters.
Speaking to the star-studded crowd at the BAFTAs, an overjoyed Affleck stated his role behind the camera has rejuvenated his Hollywood career.
He said, ""This is a second act and you've given me that, this industry has given me that. So I'd like to dedicate this award to anyone else who is looking for their second act.""
Affleck's Argo won three awards altogether - it also picked up the prize for Best Editing.
In the acting categories, Daniel Day-Lewis continued to rule over the 2012/2013 awards season by picking up the Best Actor trophy for his turn as U.S. President Abraham Lincoln in Lincoln, while French screen legend Emmanuelle Riva took home the Best Actress award for her portrayal of a tragic stroke victim in Amour.
Anne Hathaway (Les Miserables) and Christoph Waltz (Django Unchained) triumphed in the Best Supporting Actress and Actor categories respectively, and director Sir Alan Parker was was handed the Academy's highest honour, the BAFTA fellowship, in recognition of his career achievements. He followed in the footsteps of fellow filmmakers Martin Scorsese and Steven Spielberg.
The event was held at London's Royal Opera House and was hosted by British comedian Stephen Fry.
The full list of winners are as follows:
Best Film - Argo
Outstanding British Film - Skyfall
Director - Ben Affleck (Argo)
Leading Actor - Daniel Day-Lewis (Lincoln)
Leading Actress - Emmanuelle Riva (Amour)
Supporting Actor - Christoph Waltz (Django Unchained)
Supporting Actress - Anne Hathaway (Les Miserables)
Outstanding Debut by a British Writer, Director or Producer - Bart Layton, Dimitri Doganis (The Imposter)
Documentary - Searching For Sugar Man
Original Screenplay - Quentin Tarantino (Django Unchained)
Adapted Screenplay - David O. Russell (Silver Linings Playbook)
Film Not In The English Language - Amour
Animated Film - Brave
Original Music - Thomas Newman (Skyfall)
Cinematography - Claudio Miranda (Life Of Pi)
Editing - William Goldenberg (Argo)
Production Design - Eve Stewart, Anna Lynch-Robinson (Les Miserables)
Costume Design - Jacqueline Durran (Anna Karenina)
Sound - Simon Hayes, Andy Nelson, Mark Paterson, Jonathan Allen, Lee Walpole, John Warhurst (Les Miserables)
Special Visual Effects - Bill Westenhofer, Guillaume Rocheron, Erik-Jan De Boer, Donald R. Elliott (Life of Pi)
Make-up & Hair - Lisa Westcott (Les Miserables)
Short Animation - The Making Of Longbird
Short Film - Swimmer
Orange Rising Star Award - Juno Temple
Fellowship Award - Sir Alan Parker