At a young age, the Prime Minister had received spiritual guidance from the monk, who passed away at the age of 98. He had been undergoing treatment for age-related ailments since February, 2015.
A statement released by the Ramakrishna Math and Ramakrishna Mission, Belur Math, said, "Despite the best medical attention, his condition deteriorated over the last few days and he passed away around 5.30 PM today at Ramakrishna Mission Seva Pratishthan hospital."
The cremation will take place at Belur Math tomorrow at about 9.30 pm and the gates of Belur Math would remain open tonight and tomorrow till the last rites were completed, it stated.
As a young boy, PM Modi had visited the Belur Math to join the Order, but his request was turned down and he was told that his calling was elsewhere. Later, he got spiritual guidance from Swami Atmasthananda in Rajkot, Gujarat.
Chief Minister Mamata Banerjee, who paid a visit to the ailing monk earlier in the afternoon, also condoled the death of the monk, describing his passing away as "an irreparable loss to the mankind".
"Saddened that Rev. Swami Atmasthanandaji, President, Ramakrishna Math & Mission passed away today at Seva Pratishthan #Kolkata," she tweeted.
Atmasthanandaji, born in May, 1919, at Sabajpur, near Dhaka, now in Bangladesh, had received "mantra diksha" from Swami Vijnananandaji Maharaj (a monastic disciple of Ramakrishna) in 1938 and joined the Ramakrishna Order at Belur Math in January, 1941 at the age of 22.
He was elected president of the Ramakrishna Math and Ramakrishna Mission in December 2007.
Swami Atmasthanandaji had travelled extensively all over the country and abroad and visited several branches of the Order and some unaffiliated centres spreading the messages of Ramakrishna, Sarada Devi, Swami Vivekananda and Vedanta, besides giving 'mantra diksha' to disciples.
He was one of the key persons to organise the Pallimangal (integrated rural development) activities in Kamarpukur and Jayrambati, a youth training centre at Saradapitha (Belur) and many other social service programmes.