The celebrated singer, musician, poet and composer had a career spanning almost seven decades, renowned in the Somali community worldwide for his songs of peace and patriotism.
Naji had fled his homeland in 1991 when civil war broke out, and found his permanent home in London, returning only occasionally to Somalia, local media reports said.
President Hassan Sheikh Mohamud described him as a "heavyweight Somali musician who was greatly respected by the Somali people".
"He had an immense role in the development of Somali literature, patriotism and culture," he said in a statement.
Media reports in Somalia said he had died in London on Monday after an illness.
"Deeply saddened by the loss of Ahmed Naji Sa'ad, a true icon in Somali arts. His brilliance as a composer, singer, musician, and teacher will forever be remembered," Somalia's Information Minister Daud Aweis said on X, formerly Twitter.
Naji was born in Mogadishu in 1939 and found his love of music while still at school before starting a fully-fledged musical career in 1954.
Abdullahi Mohamed Abukar, a Somali songwriter who had worked with Naji, said he was "one of the greatest musicians of Somalia".
"He fled the country when the civil war broke out, but he never stopped caring for his country and people, he has composed so many songs while a refugee outside the country, songs that encouraged peace and unity for Somalis," he told AFP.
"He was always optimistic and prayed for the country in his songs," he added.
Abdullahi said Naji joined Radio Mogadishu after Somalia gained independence, becoming director of the music department, and media reports said he had continued to be a regular feature on the station's programmes.
"Very sad to learn of the passing of Ahmed Naji Sa'ad, a beloved artist who contributed so much to Somalia's cultural scene," UN mission chief in Somalia, Catriona Lang, said on X.