His wife Amanda Miguel wrote on Instagram: "With absolute sadness, we regret to inform the public and friends that our dear Diego left his beautiful body today, to continue his path and creativity into another form of eternal life. For.
"The whole family goes through this pain, so we appreciate your understanding during this difficult time."
According to DW, the Argentine icon reportedly fell ill with Covid in December and had to be hospitalised.
Two hours before his death, Verdaguer took to Twitter to thank his wife of 47 years.
"I will never get tired of dedicating this to you! You are and will be the thief who stole my heart @amandamiguels," he wrote.
Verdaguer died on Thursday in Los Angeles, California and is expected to be cremated.
Born Miguel Attilio Bocadoro Hernández on April 26, 1951, in Buenos Aires, Verdaguer had both Argentine and Mexican citizenships.
He entered the field of music at the age of 17 and rocketed to fame years later with hits such as Chiquila, Pajaro Que Eti, Volo, Volver, La Ladrona.
He was known for playing the trumpet and bandoneon and received many awards in his 50-year career, including an award from the Mexican Society of Authors and Composers, while his Italian roots influenced his musical style.
Tributes have begun for the beloved singer.
Mexican musician Lucero said Verdaguer's legacy will live on as he paid tribute to his career.
"My heart breaks at this devastating news," Sofia Milos said. "Rest in Peace My Friend Diego."
One fan wrote: "RIP, Diego Verdaguer. What a legend in the Spanish community with his songs."
Another said: "RIP Diego Verdaguer. You were a big part of my childhood."
The third wrote, "Diego Verdaguer died and I'm crying. My dad watched him play and I listen to 'coco loco' constantly."