Contrary to what you may have heard, The Book of Mormon is not the second coming.

But it is a raucously entertaining and exhilarating musical comedy that is impossible to resist. Written by South Park creators Trey Parker and Matt Stone along with Robert Lopez of Avenue Q fame, this show wins you over with its combination of cheeky outrageousness and theatrical savvy.

Much of the credit for the latter must no doubt be accorded Casey Nicholaw (The Drowsy Chaperone), who choreographed and co-directed the show with Parker.

Parker and Stone have previously demonstrated their affinity and chops for musical comedy with their early film Cannibal! The Musical and South Park: Bigger, Longer and Uncut, the feature version of their iconic TV show. But they have outdone themselves here, creating a satirical musical about the Church of Latter Day Saints that manages to be simultaneously irreverent, scatological, and sweetly old-fashioned.

The show depicts the misadventures of a pair of Mormon missionaries, golden boy Elder Price (Andrew Rannells) and slovenly, pudgy Elder Cunningham (Josh Gad), when they are assigned to a poverty-stricken Ugandan village.

Needless to say, culture shock ensues, with the hapless pair confronted with natives beset by such issues as extreme poverty, female genital mutilation, an AIDS epidemic, widespread rape and slaughter, and a hostile warlord. No wonder that they greet each other with the phrase “Hasa Diga Eebowai,” which roughly translates to “Fuck you, God.”

Elder Price, who had dreamed of being sent to the paradise that is Orlando, Florida, is quickly overwhelmed by the conditions. But his partner is eager to take up the cause, particularly looking forward to the opportunity to personally baptize the beautiful native girl Nabulungi (Nikki M. James).

The show reveals plenty of research on the part of its creators with its plethora of jokes about Mormon history and protocol, including a wacky depiction of Joseph Smith’s encounter with the Angel Moroni and a mock Biblical pageant that must be seen to be believed.

While the sprightly score is more serviceable than memorable, it features plenty of fun production numbers that are enlivened by the riotous lyrics and energetic choreography featuring the clean-cut missionaries cutting loose with go-go style abandon.

A particular highlight is the “Mormon Hell Dream,” featuring a cast of costumed characters including Satan, Jeffrey Dahmer and Gehnghis Khan, Hitler and Jeffrey Dahmer.

As with most relentlessly comic shows of this type, not all of the jokes land. Some are repeated to the point of exhaustion, and others simply feel cheap or exploitative. But thankfully there are far more hits than misses, and musical comedy aficionados will especially appreciate the parodic references to shows ranging from The Lion King to The King and I.

There are sight gags in abundance, from the statue of the Angel Moroni atop the proscenium to the dead animal carcasses dragged across the stage. Set designer Scott Pask and costume designer Ann Roth score consistent laughs with their wildly imaginative contributions.  

The ensemble is terrific, with Gad resembling a sweeter John Belushi as the hapless Cunningham and Rannells especially winning as his mortified counterpart. James is sweetly appealing as the native girl eager to embrace the new religion, while Michael Potts brings a sardonic comic edge to his village leader.

That a show featuring a character’s repeated refrain that “I have maggots in my scrotum” could manage to be so endearing is something of a miracle in itself. There will certainly be those who find The Book of Mormon more sophomoric than funny. But judging by the gales of laughter that rocked the packed theater, there probably won’t be too many of them.

Eugene O’Neill Theatre, 230 W. 49th St. 212-239-6200. www.telecharge.com.