Johannsson won a Golden Globe and received an Academy Award nomination for his score for the James Marsh-directed film "The Theory of Everything", starring Eddie Redmayne as celebrated theoretical physicist Stephen Hawking.
He secured another Academy Award nomination for his score in the Denis Villeneuve-directed crime thriller "Sicario".
Johannsson had frequently collaborated with Villeneuve, providing background score to his films "Arrival" and "Prisoners".
Redbird Music Management, the company that represents the Icelandic composer, also announced his death on Facebook.
"It is with profound sadness that we confirm the passing of our dear friend Johann Johannsson.
"We have lost one of the most talented and brilliant people who we had the privilege of knowing and working with. May his music continue to inspire us," the post read.
"Mandy" and "Mary Magdalene" are the last two films for which Johannsson gave the score.
He is survived by his parents, sisters and daughter.
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