Tommy McLain, a son of the Louisiana bayou whose distinctive tenor laid over a bouncy blend of rock, zydeco, country and R&B made him the king of swamp pop in the 1950s and ’60s and later earned him a following among artists like Elvis Costello and Nick Lowe, died on July 24 in Hessmer, La. He was 85.

His death, in a nursing facility, was announced by his family in a statement. No cause was given.

Swamp pop emerged in the late 1950s as Louisiana musicians playing rock ’n’ roll incorporated elements of their native zydeco and blues, along with the singular influence of Fats Domino and his rollicking piano sound.

“Despite the fact they were singing rock ’n’ roll, they imbued it with this French Cajun feeling, which, coupled with Fats Domino’s sound, gave it a unique sound,” the music historian John Broven, the author of “South to Louisiana” (1984), said in an interview. “Tommy was very much part of that.”

Mr. McLain started off playing in swamp pop bands like the Vel-Tones and the Boogie Kings and then went solo in the mid-1960s.

Though he was a prolific songwriter, his biggest hit, released in 1966, was a cover: “Sweet Dreams,” a song written by Don Gibson that had been a hit for Patsy Cline in 1963.

Mr. McLain had practically stumbled on the song. Driving to a show, he heard the Cline version on the radio. He began to sing along and decided to perform it that night.

He eventually got a studio owner, Floyd Soileau, to record it. But Mr. Soileau found it too offbeat a track and hesitated to release it; he sold it instead to the owner of a nearby brothel.

A few days later, the brothel owner called.

“Floyd, God almighty, do you have a hit,” Mr. Soileau recalled the owner saying, recounting the moment in an interview with Mr. Broven for his book. “That ‘Sweet Dreams’ does not quit playing on the jukebox in that house. Them women just play this thing over and over again, and the women really know what’s going to sell a record.”

Mr. McLain’s version climbed to No. 15 on the Billboard Hot 100 — higher than Patsy Cline’s version had reached.

By then swamp pop was in decline, pushed aside by the radio dominance of rock bands from Britain and the East and West Coasts.

But it found a following in Britain, where in 1974 the D.J. and label owner Charlie Gillett released “Another Saturday Night,” a compilation of swamp pop that included a track by Mr. McLain. Early punk musicians tuned in to Mr. McLain’s offbeat sound, as did Mr. Costello and Mr. Lowe.

In time, a new generation of American musicians and fans discovered Mr. McLain as well. In the 2010s, he performed with Lil’ Band O’ Gold, a swamp-pop group led by the singer and guitarist C.C. Adcock.

“He had an amazing, one-of-a-kind, extraordinary X factor — whatever you call it — of a voice,” Mr. Adcock said in an interview. “It didn’t sound like ‘oh, that’s a white dude singing well,’ or ‘that’s soul music.’ It just sounded like that weird thing that I think only a few people have.”

In 2022, Mr. McLain released his first album in more than 40 years, “I Ran Down Every Dream.” He had help from his friends: Mr. Adcock got him the contract; Mr. Costello wrote one song with Mr. Adcock, “My Hidden Heart,” and wrote the title track with Mr. McLain; and Mr. Lowe collaborated with him on another track, “The Greatest Show on Hurt.”

Both Mr. Lowe and Mr. Costello sing on the album, along with other musical luminaries like Ivan Neville and Van Dyke Parks.

“I’ve got to have music around me,” Mr. McLain told NPR in 2022. “That’s all I know. That’s my gift, you know? So I talk to everybody about music, and they talk about whatever they do, and I don’t understand a word they’re saying because music’s all I can do.”

Thomas Murray McLain was born on March 15, 1940, in Jonesville, La., in the east-central part of the state. He grew up in nearby Pineville, along the Red River. His father, Glen, was a Baptist minister who looked skeptically on his son’s early musical interests but nonetheless consented to getting him a guitar when he was just 5. His mother, Nellie (McGurk) McLain, was more open to his potential as a musician and encouraged him to join a string of local bands while still in high school.

While developing his career as a singer and musician, Tommy wrote songs for other performers, including “If You Don’t Love Me Alone (Leave Me Alone),” a hit for the Tejano singer Freddie Fender in 1977.

Mr. McLain continued to record and tour through the 1970s. But the venues that would have him shrank in number and size, until he was mostly playing lounge matinees in suburban Louisiana.

He was also, by his own admission, having problems with drugs and alcohol. Eventually he got clean and converted to Roman Catholicism.

“Elvis Presley and Hank Williams should have had my life,” he told Town Talk, a Louisiana publication, in 2006. “And I should have had their money.”

He is survived by his sons, David, Barry, Chad and Jonathan; his daughters, Felicia Soileau and Alyson Lemoine; his brother, Paul; his sisters, Glendola Mills and Odessa Lewis; 10 grandchildren; seven great-grandchildren; one great-great-grandchild; and his partner, Carol Skaggs.

Mr. McLain’s recent album brought him national attention — he and Mr. Adcock performed on “The Late Late Show With James Corden” in 2022, and he recently joined Lucinda Williams in a duet, “Release Me,” for the album “A Tribute to the King of Zydeco, Clifton Chenier.”