A dazzling snow globe of a set and an infectiously gleeful portrayal of childlike wonder make “Elf The Musical” at The Music Hall in Portsmouth a lesson in the magic of Christmas.

To run through Dec. 16, the show is the latest collaboration between the theater and The Ogunquit Playhouse of Maine. It’s based on the hit 2003 movie that starred Will Ferrell as the exuberant, good-hearted Buddy, who was raised as an elf but has trouble fitting his over-sized frame into life at the North Pole. When he learns he’s actually human, he goes in search of his biological father, a harried New York City book publisher with little time for family or holiday spirit.

It must be a daunting prospect to take on a role so tied to Ferrell’s frenetic enthusiasm, which fueled “Saturday Night Live” skits before hitting the big screen in comedies including “Old School” and the “Anchorman,” “Daddy’s Home” and “Zoolander” films. But New York and Broadway veteran Steven Booth, decked out in Buddy’s signature yellow tights and green elf suit, adeptly wears that awkward eagerness in the musical version of “Elf.” It’s a wide-eyed awe that often wanders into confusion, and it makes the audience root even more for him to find a place he truly belongs.

That and prove once and for all that “the best way to spread Christmas cheer is singing loud for all to hear.”

Booth previously starred in the first national tours of “Kinky Boots” and “Happy Days” and on Broadway has performed in “School of Rock,” “Glory Days” and “Avenue Q.”

An innovative stage set crafted by noted New York-based scenic designer Jason Sherwood, who has been working with Grammy Award-winning singer Sam Smith on his tour, does more than frame the “Elf” story. Scenes shift and settle like snow inside a shaken snow globe. Gone is the traditional boxed shape of the stage, replaced by rounded edges that crackle with an icy warmth and add to the sense of blurring realities. Projections blink into scenes overhead and to the sides of the stage, while raised and lowered backdrops materialize and then disappear as the story shifts from the gear-driven toy factory at the North Pole to Walter Hobbs’ bustling office to the festively decorated Rockefeller Center skating rink.

The clever use of space keeps the audience inside the fantasy realm, but it’s clear from the constant motion that it requires seamless timing on stage and in the wings. Broadway director and choreographer Connor Gallagher guides the production, which both stays faithful to some beloved “Elf” bursts of optimism (“I just like to smile. Smiling’s my favorite”) and introduces some new gags, references and story elements to update the story.

The musical numbers, too, flesh out the character development, with one particularly entertaining number featuring dejected off-duty store Santas at a Chinese food restaurant. Christmas cheer, indeed, is in short supply, and they’ve got the Broadway-esque jazz hands to prove it.

Jen Cody is a laugh-getter as Deb, Walter Hobb’s secretary who runs the office with an effortlessly upbeat efficiency. Cody also has starred in numerous Broadway productions, done voice work for animated movies and performed on television in CBS’ “Instinct,” “Bull,” “Unforgetable” and “Blue Bloods.”

A sweet note is Calvin Middleton, in his professional debut, as 12-year-old Michael Hobbs. His crystalline vocals were an earnest counterpoint to anyone who harbors doubts about Buddy or Santa Claus. That includes Walter Hobbs, played by Christopher Russo, who also starred in Madison Square Garden’s production and a national tour of “Elf The Musical.”

Look for turns from Diana Huey as Buddy’s love interest Jovie, Lothair Eaton as the Macy’s department store manager, Annie Edgerton as Emily Hobbs, Blake Hammond as Santa and Philip Paul Kelly as Mr. Greenway.