What the world probably doesn’t need right now is one more big-screen adaptation of an all-but-forgotten TV series. Another buddy-cop flick? Yeah, we could get along just fine without that, too. But “21 Jump Street” qualifies as a happy surprise, a bad idea that turns out to be an often uproariously funny movie.

The original series, which was one of the Fox network’s first offerings, aired back in the days when Tiffany and Debbie Gibson were topping the charts; that gave its premise — a team of youthful-looking police officers infiltrating the teen scene to fight crime — a touch of trendiness. More than 20 years later, “Jump” is only remembered for introducing America to Johnny Depp (OK, perhaps there are still a few sad souls out there who like to reminisce about co-star Richard Grieco’s brief reign as a heartthrob).

One of screenwriter Michael Bacall’s savviest moves is to turn the show’s concept inside out: In the film, Channing Tatum and Jonah Hill — neither of whom looks like he just got his drivers’ license — play all-but-incompetent Metropolitan City lawmen who are shifted into a recently revived “cancelled undercover police program from the ‘80s.” The deadly designer drug HFS is all the rage at Sagan High, and swaggering lunkhead Jenko (Tatum) and former juggling society member Schmidt (Hill) are assigned to take it off the market by enrolling as students.

The masquerade is absurd, and directors Phil Lord and Christopher Miller know it. “Jump” gets off on the right foot as soon as Schmidt and Jenko step onto the campus and quickly realize how much adolescent culture has changed since their senior year.

“I totally know the cause,” Jenko grimly announces. “‘Glee.’”

The dim-bulb detectives don’t exactly blend with the various cliques they’re supposed to be cracking — ecologically minded do-gooders, science geeks, self-dramatizing drama students whose teacher tells them, “You never know what you can’t achieve until you don’t do it,” etc. — prompting several profane tirades from their captain (an enthusiastically obnoxious Ice Cube) and numerous opportunities for Hill and Tatum to turn up the comic heat. They’re an unexpectedly dynamic team, with Tatum effectively underselling most of his lines while Hill puts a frantic, semi-touching spin on the idea of a former high school loser grasping at a second chance to be part of the popular crowd.

The stars’ complete commitment to the material seems to carry over to the sensational supporting cast, which includes expert turns from Rob Riggle as a slightly warped tough-guy teacher and Brie Larson as the hapless cutie who falls for Schmidt. The true breakout performance, however, comes from Dave Franco as a suave student leader with some very unsavory habits and a determination to avoid being busted. “You know what happens to a handsome guy like me in jail?” he yelps. “It rhymes with ‘grape’!”