LOS ANGELES — John Hillerman, who played stuffed-shirt Higgins to Tom Selleck’s freewheeling detective Thomas Magnum in the 1980s television series ‘‘Magnum, P.I.’’ died Thursday of natural causes at his home in Houston. He was 84.

Mr. Hillerman had been in declining health, his nephew Chris Tritico said.

Besides playing manager of the Hawaiian estate that Magnum used as home base, Mr. Hillerman was known for his 1970s roles as arrogant radio show detective Simon Brimmer on the ‘‘Ellery Queen’’ series and the difficult boss on the sitcom ‘‘One Day at a Time.’’

When Mr. Hillerman decided to retire about 17 years ago, the actor returned to his native state of Texas and was content leaving Hollywood behind, said his nephew.

Tritico remembered his uncle, an Air Force veteran, fondly.

‘‘He had an outstanding sense of humor and was one of the most well-read people I ever met. You couldn’t play Scrabble with him,’’ Tritico said.

As for that quasi-British accent that Mr. Hillerman used on ‘‘Magnum’’ and elsewhere, his nephew said that was honed during several decades of playing varied roles on the New York stage before he turned to TV and movies.

Mr. Hillerman used something closer to his own voice in Mel Brooks’s ‘‘Blazing Saddles,’’ playing Howard Johnson, one of the comic Western’s many Johnsons.

He appeared in a number of TV series, including ‘‘Valerie,’’ ‘'The Love Boat,’’ and ‘‘The Betty White Show,’’ and in films including ‘‘The Last Picture Show’’ and ‘‘High Plains Drifter.’’

His last credits included 1996’s ‘‘A Very Brady Sequel’’ and an early ‘90s appearance on ‘‘Murder, She Wrote.’’

The role of Higgins was his favorite, Tritico said.

‘‘The reason he didn’t take another big role is he refused to take a sitcom after ‘Magnum,'’’ he said. ‘‘He wanted to continue doing the serious work that he felt ‘Magnum’ was.’’

Mr. Hillerman’s survivors include a sister, Jo Ann Tritico, and six other nieces and nephews.

At his request no services will be held, Chris Tritico said.