Koenig died on Monday at his home in the North Hollywood neighbourhood of Los Angeles, talent agent Zachery McGinnis said in a statement.
His death was also announced in a Facebook post by talent agency Galactic Productions, which said he "passed of old age at home in North Hollywood last night surrounded by his daughter and niece".
The message described Koenig's legacy as an actor and praised his "talent, warmth, and unforgettable performances" which have "left a lasting mark on generations of fans around the world".
In Star Trek, Ensign Chekov was the sole Communist-bloc member of the spaceship Enterprise bridge staff.
His friendly, supportive presence showed how the rival nations (in the far-off future in which the show was set) were capable of working together.
Speaking Russian-accented English, Chekov embodied stereotypical Russian personality traits, including fierce pride, love of poetry and blind loyalty.
Star Trek ran on NBC from 1966 to 1969 and has had an almost unprecedented afterlife as fans, or Trekkies, kept interest in the show alive.
Koenig was born September 14, 1936, in Chicago, the son of a businessman.
He graduated from the University of California, Los Angeles in 1958, then studied acting at New York's The Neighborhood Playhouse for two years. He began getting television roles in the early 1960s, appearing on Mr Novak and Ben Casey.
"My heart is heavy," Koenig's castmate, George Takei, who played Hikaru Sulu, said in a post on the social platform X.
"Walter was more than Chekov. He was a writer, a teacher, a thoughtful man, and a loyal friend."
Koenig was the best man at Takei's 2008 wedding to Brad Altman, his partner of more than two decades.
"Walter's legacy extends far beyond the screen. Through countless convention appearances and interactions with fans, he shared his kindness, wit, and appreciation with everyone fortunate enough to meet him.
"He understood what Star Trek meant to people and embraced the community that grew around it," McGinnis said.
"Thank you, Walter, for the memories, the inspiration, and for boldly going where few have gone before."
Koenig's son, Andrew, was also an actor, best known for playing Boner on the sitcom Growing Pains. Andrew Koenig died in 2010 at 41. Walter Koenig said his son had taken his own life.
Koenig played Chekov in seven Star Trek movies starting in 1979, as well as innumerable other spinoffs, including writing a Star Trek book, Chekov's Enterprise, in 1980.
The TV show has also inspired two spinoff TV series with new casts, and conventions that draw thousands of fans.
After Star Trek ended, Koenig continued acting and wrote scripts for Family, The Incredible Hulk and other shows. He also taught part time at UCLA and other schools.
Koenig also worked in the burgeoning field of computer games, including some with a Star Trek theme. In 1995, he took a role in the CD-ROM game Maximum Surge.
"I'm at a point where I could opt in my life for complacency and a bit of predictability, or I could have one last holler - one last try for adventure," Koenig told The Associated Press in 1995.
"I'm of the opinion that adventure is still a very enticing and exciting option."
He returned to the science fiction genre with occasional appearances in the syndicated 1990s TV series Babylon 5.
Koenig's death leaves William Shatner, who played Captain James T. Kirk, and Takei as the only surviving members of the original series' main cast.
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