“Sweeney Todd: The Demon Barber of Fleet Street” is the quintessential Tim Burton movie, even though it springs from somebody else’s celebrated mind.

Everything about Stephen Sondheim’s revered musical, which provided the inspiration for the film, seems tailor-made for the director’s sensibilities. Truly, what other filmmaker could tell the story of a vengeful barber (Johnny Depp) who slits his customers’ throats and the lovesick baker (Helena Bonham Carter) who grinds up the dead bodies for her meat pies?

It’s strangely beautiful and beautifully strange, with horrific subject matter that produces plenty of wicked humor and characters who initially seem ghoulish but ultimately reveal themselves as sympathetic and deeply sad.

Burton fell in love with Sondheim and Hugh Wheeler’s 1979 work when he saw it 20 years ago in London, and it shows.

The absurdity, loneliness and darkness that infuse the best of Burton’s oeuvre — “Edward Scissorhands,” “Ed Wood” and “Corpse Bride,” all of which starred his longtime friend and collaborator Depp — seem heightened here. Burton’s vision of 19th century London, created with the help of cinematographer Dariusz Volski and production designer Dante Ferretti, is vividly gritty, full of strikingly contrasting blacks and grays punctuated by dramatic splashes of red.

That would be the blood, of course.

It sprays like a fire hose from the necks of Sweeney’s unsuspecting victims, who are then dumped down a chute and into Mrs. Lovett’s meat grinder. Watching Sweeney do this over and over — passionately but methodically with the help of his “friends,” his ornate silver razors — is at once harrowing and hilarious.

Sweeney, formerly known as Benjamin Barker, goes on his killing spree after spending 15 years in an Australian prison on false charges. The villainous Judge Turpin (Alan Rickman, always a subtly delicious bad guy) sent Sweeney away to steal his bride and baby girl. The wife has long since poisoned herself and young Johanna (Jayne Wisener), now Turpin’s ward, is kept like a fragile bird in a cage in his elegant home.

Once he dispatches his first victim — the Italian huckster Pirelli, played by a scene-stealing Sacha Baron Cohen in tight blue pants that leave nothing to the imagination — Sweeney doesn’t know what to do with him and stuffs him in a trunk. But the ever-practical Mrs. Lovett, who famously makes “the worst pies in London,” sees the body and instantly gets an idea of how to improve her product. (Her cheery line about how “everybody shaves, so there should be plenty of flavors” is a twisted classic.)

As the carnage piles up and their relationship evolves, it turns unexpectedly sweet. Sweeney and Mrs. Lovett fall into an easy rhythm, but he’s too focused on his goal — slicing Turpin’s throat — to realize she’s in love with him and dreams of building a simple life with him and the orphaned Toby (Edward Sanders), who helps out around the shop. Bonham Carter is no Angela Lansbury, who originated the role on Broadway, or Patti LuPone, who took it over in a 2005 revival, but she absolutely has the right look for the part and a touching tinge of melancholy.

Depp, meanwhile, has been immersing himself in challenging roles like Sweeney Todd his whole life, and is just as snug a fit for the material as Burton himself. With his shock of black-and-white hair and obsessed look in his darkened eyes, Depp’s Todd could be a long-lost relative of Edward Scissorhands.

Perhaps some of the emotions have been lost in cutting a three-hour stage production down to a two-hour movie. When Sweeney’s traveling companion Anthony (Jamie Campbell Bower) instantly falls for Johanna from afar and promises in song, “I’ll steal you,” it comes out of nowhere and rings hollow.

Ironically, these two young performers, who have some of the smallest amounts of screen time, are the only ones who impress with their voices. Depp and Bonham Carter aren’t exactly musical theater veterans — they’re acting the music more than singing it a lot of the time, though that does make “Sweeney Todd” more raw.

But it’s no small feat what Burton has accomplished in creaing a captivating movie musical; making the transition from Broadway to the big screen has proven an iffy proposition in recent years. “Dreamgirls” dazzled and “Chicago” won the Oscar for best picture with big stars bursting from each, but they’re the exceptions.

Everyone could sing — really, really sing — in Joel Schumacher’s version of “The Phantom of the Opera” and in “Rent,” which retained much of its original stage cast. And that didn’t exactly make either of them a smashing success, now did it?

“Sweeney Todd: The Demon Barber of Fleet Street,” a DreamWorks and Warner Bros. Pictures release, is rated R for graphic bloody violence. Running time: 117 minutes. Three stars out of four.

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Motion Picture Association of America rating definitions:

G — General audiences. All ages admitted.

PG — Parental guidance suggested. Some material may not be suitable for children.

PG-13 — Special parental guidance strongly suggested for children under 13. Some material may be inappropriate for young children.

R — Restricted. Under 17 requires accompanying parent or adult guardian.

NC-17 — No one under 17 admitted.