Everybody loves a rags-to-riches story. The joyous new musical “Jersey Boys” doubles down on that favorite theme. It follows falsetto superstar Frankie Valli and the Four Seasons from working-class beginnings to Top 40 success, back down the charts, then up again to comeback glory and the Rock and Roll Hall of Fame.

The production (co-written by Marshall Brickman, who co-wrote “Annie Hall” and “Manhattan”) has been a Broadway phenomenon since 2005. What’s not to love? The sort-of-true account bounces from mob debts to family friction, drug deaths to neat-freak quarrels over hotel towels. And given the group’s impressive catalog, you’re never more than 10 minutes from a showstopper like “Sherry,” “Rag Doll” or “Walk Like a Man.” Those are some seriously golden oldies.

The film adaptation, with rock-solid direction from Clint Eastwood (of all people), should delight even millennials who think My Chemical Romance put the Garden State on the music map.

This stranger-than-fiction band biography is pop history told in four-part harmony. Like Scorsese-sassy “Goodfellas” gangsters hijacking the story, each member of the band tugs our sleeve, saying, “Don’t listen to those guys. I’ll tell you what really happened.” We begin with cocky Tommy DeVito (Vincent Piazza), aspiring guitarist, small-time crook and the group’s self-appointed organizer, talking directly to the camera and promising the inside scoop. He gives you the sense that he originated the group right after he hung the moon. He would have been as happy to be the next Al Capone as the next Sinatra.

He’s entertaining company in the way exasperating egoists can be, but before he can wear out his welcome we’re introduced to Francis Castelluccio, aka Frankie Valli (John Lloyd Young). He’s an endearing schlemiel endowed with a thrilling voice. Like bass vocalist Nick Massi (Michael Lomenda), the self-described Ringo of the group, Valli probably would have settled for weekend gigs in Newark bowling alleys. The group doesn’t take off until the arrival of business-savvy songwriting genius Bob Gaudio (Erich Bergen), who hears Valli’s hearty high notes and declares, “I had to write for that voice.”

The quartet wends its way through the challenges of launching a recording career. There’s a very funny musical tour through the Brill Building’s hit factory of producers before the boys land with Bob Crewe (Mike Doyle), depicted here as a gay party animal with an impeccable ear for sophisticated harmonies. Through it all, Valli has the kindly counsel of Angelo “Gyp” DeCarlo (the priceless Christopher Walken), a real-life Jersey mob boss who’s moved to tears by the singer’s sentimental crooning. Soon they’re selling records like the Beatles, dallying with groupies and enduring the emotional hardships of life on the road. Their troubles ratchet up several notches when they discover that bad boy DeVito has been keeping staggering debts a secret from the others.

The performers aim to give us a bit more sincerity and emotional depth than the typical band of pop impersonators, and they deliver. “Jersey Boys” is a model of light, crowd-pleasing, song-propelled pop entertainment. To borrow a line from a Crewe/Gaudio lyric, it’s just too good to be true.