A statement from the sheriff said deputies had found the 95-year-old actor and Arakawa, 64, deceased on Wednesday afternoon about 1:45pm (local time).
"Foul play is not suspected as a factor in those deaths at this time, however exact cause of death has not been determined. This is an active and ongoing investigation by the Santa Fe County Sheriff's Office," it said.
Hackman, a former Marine known for his raspy voice, appeared in more than 80 films, as well as on television and the stage during a lengthy career that started in the early 1960s.
He earned his first Oscar nomination for his breakout role as the brother of bank robber Clyde Barrow in 1967's "Bonnie and Clyde." He was also nominated for best supporting actor in 1971 for "I Never Sang for My Father".
It was his turn as Popeye Doyle, the rumpled New York detective chasing international drug dealers in director William Friedkin's thriller "The French Connection", that assured his stardom and a best actor Academy Award.
He also won a best supporting actor Oscar in 1993 as a mean sheriff in the Clint Eastwood western "Unforgiven", and was nominated for an Academy Award for his turn as an FBI agent in the 1988 historical drama "Mississippi Burning".
Hackman could come across on the screen as menacing or friendly, working with a face that he described to the New York Times in 1989 as that of "your everyday mine worker".
Born in San Bernardino, California, on January 30, 1930, Hackman's family moved to Illinois when he was a child. His father, a newspaper press operator, abandoned the family when Hackman was a teenager. The future actor remembered seeing his father wave as he drove away, instinctively knowing he would not come back. His mother later died in a fire.
"Dysfunctional families have sired a number of pretty good actors," he once said.
He joined the Marines at 16, lying about his age so he could get in, and later studied journalism at the University of Illinois. After a short stint as a television technician and administrator, he studied acting at the Pasadena Playhouse in California alongside Dustin Hoffman.
Both actors, who were voted least likely to succeed, eventually moved to New York where they worked odd jobs, chased parts and palled around with another then-struggling actor named Robert Duvall.
Hackman appeared on Broadway in "Barefoot in the Park", and "Any Wednesday". A bit part in a low-budget movie, "Mad Dog Coll" (1961), was followed by a critically acclaimed supporting role in "Lilith" (1964), starring Warren Beatty.
The actor, who shunned celebrity, starred in "Hawaii" (1966) and three lesser-known films before Beatty cast him in "Bonnie and Clyde". He varied his roles from a ski coach in "Downhill Racer" (1969) and a skydiver in "The Gypsy Moths" (1969) to an astronaut in "Marooned" (1969).
A method actor, he drew from his personal experience to flesh out a role. His characters were sometimes raw and violent and ranged from a small-town basketball coach in the 1986 sports film "Hoosiers" to Superman's archrival Lex Luthor.
Acting honors apparently did not mean much to Hackman. In 2011, he told Time magazine he was unsure where his Oscar statuettes were.
Among critics, who uniformly praised his acting, Hackman was alternately lauded as one of the great underrated stars and criticized for abandoning good character parts in favor of leading roles.
He conceded that there was a period when he took roles primarily for the money, but still came up with notable performances such as Lex Luthor, the campy villain of "Superman" (1978) and two sequels.
Hackman also starred as a vagabond with Al Pacino in "Scarecrow" (1973), a surveillance expert in "The Conversation" (1974), an admiral in "Behind Enemy Lines" (2001) and an eccentric patriarch in "The Royal Tenenbaums" (2001).
"Even at their jauntiest, Hackman's performances have volcanic undercurrents", The Guardian newspaper said in 2002. "It might be that the secret of his singularity is that his comfort zone is a scary and volatile place."
Hackman retired in his 70s, saying the parts he was offered were too grandfatherly. His last substantial role was in the 2004 comedy "Welcome to Mooseport".
"I miss the actual acting part of it as it's what I did for almost 60 years and I really loved that," he told Reuters in 2008. "But the business for me is very stressful ... and it had gotten to a point where I just didn't feel like I wanted to do it anymore."
Living outside Santa Fe, New Mexico, Hackman was married twice and had three children - Christopher, Elizabeth Jean and Leslie Anne - with his late ex-wife, Faye Maltese, who died in 2017. He married Arakawa in 1991.
