Hoffman’s first big role was as a pot-smoking stormchaser in Twister. Not a comedic movie, but his part was as the comic relief.
How about Michael Caine? ZULU gets him the big “and introducing…” credit in '64; he graduates to leading-man status in '65, with THE IPCRESS FILE; and promptly earns a Golden Globe (Drama) nomination for ALFIE, which comes out in early '66.
That’s a pretty solid start; just note that he simultaneously earns a Golden Globe (Comedy) nomination for GAMBIT, which comes out in late '66. And he eventually gets another Golden Globe nomination for his Oscar-winning work in a Woody Allen comedy, and another for DIRTY ROTTEN SCOUNDRELS, and – okay, granted, he then soon gets another Golden Globe nomination for his dramatic Oscar-winning role in THE CIDER HOUSE RULES, but a year later he’s delivering effeminate put-downs at regular intervals for the higher-grossing MISS CONGENIALITY – and then, soon after hamming it up for an even-higher-grossing AUSTIN POWERS sequel, he’s back to earning another Golden Globe nomination for dramatic work in THE QUIET AMERICAN.
Because, well, the guy never really stopped doing dramas; he’s just perfectly capable of boogieing on over to comedy at will, is all.
Michael Caine is famous the… diversity of his films. Basically, if the check clears, he’ll take the part.
Oh, granted. But the OP merely asks for an actor “who becomes known mainly as a dramatic performer that later become successful in comedic roles.” Back in the days of ZULU and THE IPCRESS FILE and ALFIE, he became known mainly as a dramatic performer; he later became successful in comedic roles; his other films are, strictly speaking, irrelevant.
For small-screen work, Robert Culp ain’t bad; he starred in his own Western for years back in the '50s, and after playing it serious in episodes of THE OUTER LIMITS went on to play it straight with I SPY during the '60s – and then, after self-satisfiedly murdering a bunch of people as COLUMBO’s worthy opponent in the '70s, he was perfectly at home doing light comedy on THE GREATEST AMERICAN HERO in the '80s, hosting SNL before spending the '90s as the go-to guy if you need a cheerful sixtysomething to pop in and get laughs for an episode of your sitcom, be it THE GOLDEN GIRLS or WINGS or THE NANNY or EVERYBODY LOVES RAYMOND.
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- regarding Jaws: The Revenge
John C Reilly comes to mind. He used to do all sorts of dramatic roles, Hard Eight, Magnolia and then he switched into comedy - Talladega nights, Step-Brothers, Walk Hard.
Martha Plimpton has always been an indie dramatic art-house type of actress. She’s hilarious on Raising Hope, I wish she’d been doing more comedy earlier.
George Hamilton arguably counts.
You could say Fred MacMurray who did comedy roles in Disney films and “My Three Sons” after playing dramatic roles (heels) in “Double Indemnity”, “The Caine Mutiny” and “The Apartment”. Apparently he was playing light comedies before that and was more successful than I realized…the top paid film star and fourth highest paid American in 1943 according to wiki. But the “cast against type” by Billy Wilder is what his film career gets remembered today.
Also in Platoon, there was this young kid named Johnny Depp…
Shelly Winters won Oscars for The Diary of Anne Frank and A Patch of Blue. Estelle Parsons won an Oscar for Bonnie & Clyde. They later played Roseanne’s maternal grandmother and mother.
I’m surprised that no one has mentioned that great actor Eddie Albert. Who would’ve thought that he would be so funny in Green Acres after a long career in dramatic roles (twice nominated for an Oscar). And, yes, I really like the silliness of Green Acres.
Also, how about Rock Hudson? He spent the '50s making, what, half-a-dozen westerns, and half-a-dozen war films, finding time along the way to rack up an Oscar nomination for GIANT after starring in MAGNIFICENT OBSESSION and ALL THAT HEAVEN ALLOWS – and suddenly he’s in PILLOW TALK and LOVER COME BACK and COME SEPTEMBER and SEND ME NO FLOWERS and MAN’S FAVORITE SPORT?
You could make a case for Peter O’Toole, getting famous in his ultra-serious LAWRENCE OF ARABIA/BECKET/LORD JIM days before demonstrating a real flair for light comedy.
At that, how about Matt Damon? After years in supporting parts – COURAGE UNDER FIRE, SCHOOL TIES, that sort of thing – he gets his first shot at courtroom-drama leading-man status with THE RAINMAKER, instead makes GOOD WILL HUNTING his big break, follows up with stuff like ROUNDERS and SAVING PRIVATE RYAN, and otherwise becomes known mainly as a dramatic performer before later becoming successful in comedic roles, no?
It seems to me that a number of Brits get known for dramatic roles before succeeding with comedic ones: Patrick Stewart, Colin Firth, Timothy Dalton…
Thanks for that link, GIGObuster. That’s reason #7,386 I love movies - because of possibilities like Lieutenant Frank Drebin & Mayor Carmine DePesto playing Ben Hur & Messala 
UT~
I immediately thought of Russell Johnson (prolly cuz I just watch the untold story of Gilligan’s Island).
He was, primarily, a character actor in westerns and sci-fi. Most people know him as The Professor.
John Ritter, The Waltons to Three’s Company