The Four Weddings and a Funeral star said it was "a lovely surprise and a great honour" to be recognised.
Grant, 55, received his accolade at the annual BFI chairman's dinner on Tuesday at London's Corinthia Hotel.
Recent Fellowship recipients include the director Stephen Frears, with whom Grant recently worked on comic biopic Florence Foster Jenkins.
Grant, whose other hit films include Notting Hill and Love Actually, was presented his award by film producer Eric Fellner, co-chairman of Working Title.
Fellner said Grant was "one of those extraordinary British actors whose effortless performance and on-screen charm has endeared him to generations of audiences worldwide".
"His success has helped British film as a whole carve out a place in the world with a distinct quality that easily rivals the best to come out of Hollywood and other countries," he continued.
Those sentiments were echoed by BFI chairman Greg Dyke, who praised Grant's "impeccable comic timing and... unique, ironic, self-deprecating and very British charm".
"Hugh always pulls off the hardest thing of all - a seemingly effortless performance," he continued. "I can assure you it's not.
"Hugh's acting talents are prodigious and his contribution to cinema enormous.
"He is a British icon and has been making literally billions of people all over the world laugh, cry - and fall in love with him of course - for over 30 years."
Other guests at Tuesday's event included the actors Henry Cavill, Martine McCutcheon, Bill Nighy and the Oscar-winning director Tom Hooper.
Since its creation in 1983, the BFI Fellowship has been awarded to key figures in British cinema such as Laurence Olivier, Dame Maggie Smith and film-maker Mike Leigh.
It has also been presented to foreign directors including Michelangelo Antonioni, Bernardo Bertolucci and Akira Kurosawa.
Hugh Grant has been given a Fellowship by the British Film Institute (BFI) at a black-tie dinner in central London.