Of all the swagger and style that defined Elvis Presley — the gyrating hips, the clothes, the cars, the smirk of all smirks, that hair! — his collection of watches probably didn’t elicit giddy screaming across teen-dom in the late 1950s.

But “Elvis,” a new biopic of the singer’s life, celebrates it all. Directed by Baz Luhrmann (with, one assumes, the same panache that all but turned the music and the dancing into characters in films like “Moulin Rouge!” and “Strictly Ballroom”), the movie is said to be a homage to a humble man whose love of collecting and trading watches was often overlooked during his all-too-brief 42 years.

“Watches were a symbol of his success and a big part of his story, and he gathered more valuable watches as his career developed,” said Catherine Martin, the four-time-Oscar-winning costume and production designer for the film, in a phone interview from her home in her native Australia. “They were a status symbol, and yet Elvis traded and gave watches away. He would swap watches with strangers whose watches he admired. It was crazy.”

Ms. Martin, who also is a producer on the film and is married to Mr. Luhrmann, said she saw Presley’s love of watches as essential to telling his story: The way he wore and collected and traded watches reflects the image he created for himself as “the King,” but blended with his folksy roots.

“Elvis was an absolutely iconoclastic dresser, and he was always accessorizing watches,” Ms. Martin said. “He reinvented himself constantly throughout his career. We don’t think of him as shocking now, but in the ’50s it was like he was a member of the Sex Pistols.”

That radical transformation of Presley, played by Austin Butler in the film, provides much of the story line for “Elvis,” including his tumultuous relationship with his manager, Col. Tom Parker (Tom Hanks), who discovered the singer in 1955.

Watches are an ever-present, if not obvious, element in many of the film’s scenes, Ms. Martin said, particularly because Presley always put a great deal of thought into how he wore and accessorized timepieces.

“Even in the 1968 TV special, in his black leather outfit, he had a custom leather wristband made for a Bulova Accutron Astronaut,” she said, referring to Presley’s famous televised comeback concert. “A lot of the watches he wore were about technological style advances. He was always interested in what the latest watches were.”

The watch that started it all was one he owned just as he was hitting it big: the triangular Hamilton Ventura, created by the American industrial designer Robert Arbib and known as the world’s first battery-powered watch. It became a signature for Presley — showing up in a gold version in his 1961 film “Blue Hawaii” — and for the watch company, which reintroduced the “Elvis watch” in 2015 to mark what would have been his 80th birthday. (It also was seen in all four “Men in Black” movies.)

“It just happened that we didn’t end up with the ‘Elvis watch’ because it’s such an iconic watch and so well known that we didn’t want it to be a main part of the story,” Ms. Martin said. “There is so much more to tell over 40 years. I don’t want to deny that this watch was super important in the Elvis story, but watches were in general.”

One example would be the Omega Constellation he wore while stationed in Germany with the U.S. Army from 1958 to 1960. Made of pink gold with a black “sniper” dial, it was one of the originals in the Constellation line. Presley later gave it to Charlie Hodge, a friend and fellow musician.

Antiquorum auctioned the timepiece in June 2012, expecting it to fetch $10,000 to $20,000; it sold for $52,500.

And there was a second Omega Constellation, given to Presley in 1961 by his record company, RCA. The 33-millimeter white gold watch has a silver dial, with 44 round diamonds accenting the bezel, and a case back that is engraved, “To Elvis, 75 Million Records, RCA Victor, 12-25-60.” Lettering beneath the Omega logo shows that RCA purchased the watch from Tiffany & Company.

Legend has it that Presley swapped it for a fan’s watch, and the fan’s nephew put the watch up for auction with Phillips in 2018. It sold for 1.8 million Swiss francs (about $1.87 million today), making it at the time the most expensive Omega ever sold. The highest bidder: Omega itself, which added the watch to its museum collection in Bienne, Switzerland.

One watch that was prominent late in Elvis’s career was the Rolex King Midas, which has an asymmetrical case with a wide integrated bracelet and was designed by Gerald Genta, the name behind such legendary watches as the Royal Oak and the Nautilus. Concert promoters gave the Midas to Presley in 1970 for performing six days of sold-out concerts, and it is now on permanent display at Graceland, Presley’s home in Memphis, where he died in 1977.

“The King Midas is a very unusual shape, and Baz happens to own one, so Austin Butler wore that in the movie,” Ms. Martin said. “Some watches were borrowed or purchased online. Some were so valuable that it was impossible to have them on set, so we had duplicates made.”

The subject of the film, which premiered at the Cannes Film Festival last month, certainly falls into the larger-than-life category that Mr. Luhrmann and Ms. Martin seem drawn to in filmmaking (like their 2013 version of “The Great Gatsby”).

“The character arc of Elvis is fascinating, as is the fact that he was an extraordinary stylist who created his own look,” Ms. Martin said. “He became super famous super fast, and watches were important to him to show that he had made it.”