The US star had a decades-long career and won the Academy Award for best-supporting actor for his role in 2006’s Little Miss Sunshine.
Arkin had previously been nominated for an Oscar in the best supporting actor category for his part in Argo.
The actor died on Friday, 30 June, at his home in California, according to Variety.
In a joint statement, his sons Adam, Matthew and Anthony told People magazine: “Our father was a uniquely talented force of nature, both as an artist and a man. A loving husband, father, grand and great grandfather, he was adored and will be deeply missed”.
Arkin was initially turned down for his acclaimed role in Little Miss Sunshine as some of the behind-the-scenes team thought he looked too healthy and fit.
In the movie about a dysfunctional family on their way to a beauty pageant, he played a frail, foul-mouthed grandfather who was suffering from years of drug abuse.
Talking about the part in 2007, Arkin told the New York Times: “It’s the best rejection I ever got in my life – they thought I was too virile”.
Hailing from Brooklyn, he started his career on the Broadway stage, winning a Tony Award for his part in 1963’s Enter Laughing.
He landed his first Oscar nomination just three years later for best actor after a successful debut film role in the Cold War comedy The Russians Are Coming! The Russians Are Coming!
Arkin also had large roles in the 1967 film Wait Until Dark opposite Audrey Hepburn as well as in 1970s Catch-22, Edward Scissorhands in 1990 and Grosse Pointe Blank in 1997.
Younger film fans will recognise him for his part in last year’s animated hit Minions: The Rise of Gru. Arkin lent his voice to the character of villain Wild Knuckles.
He also earned Emmy nominations for the TV series The Kominsky Method, which debuted in 2018.
Throughout his long career, Arkin was very prolific, appearing in more than 100 films and TV shows nominated for four Oscars in total and was also a renowned director and author.
