'Bangabahadur', meaning Hero of Bengal, died around 7 am at Koyra village in northern Jamalpur district, about 200 km from capital Dhaka.
"We had mobilised huge manpower, provided it decent food and treatment but could not save it," a forest department official familiar with the efforts to rescue him told PTI.
Bangabahadur weighed four tonnes.
A post-mortem has been orderer, the BBC reported.
Also Read
In Bangladesh, after it was thought to have travelled for nearly 1,700 kilometres, Bangabahadur was rescued on August 11 by a forest team following six weeks of frantic efforts.
On its way from India, it was forced to stay in marshes as the highlands were occupied by flood-hit people who were unwilling to let the frightened animal share their shelters.
It appeared agitated after being tranquilised more than once and moved indiscriminately for nearly an hour before it fell into a ditch unconscious during rescue efforts.
Forest officials and villagers dragged him off the ditch.
It died as a process was underway to shift it to the Bangabandhu Safari Park from the remote village. Officials had planned to bring in two trained elephants to support the transportation.
Witnesses and people in the neighbourhood suspected that excessive tranquillising might have partly led to its death.
Without proper food it gradually lost its strength.
(Reopens FGN 18)
Shrinking natural wildlife habitat has made it difficult for animals to move to safer areas during monsoon floods. Over the past weeks, Bangabahadur was forced to travel the distance in a hostile situation due to the flooding in Assam.
A Bangladeshi official had previously said India can take it back if possible "otherwise we will keep the elephant". The official had cited two cases in 2004 and 2013 in which one attempt to return an elephant succeeded while another failed.
Forest officials said the elephant remained calm, though it showed some signs of abnormal behaviour as it was forced to live in swamps for weeks despite being habituated to hills.
Soon after it had crossed the border, the elephant grabbed media attention as it was followed by hundreds of people in boats every day requiring police deployment to keep it undisturbed.
Over the past nearly 50 days, it roamed along the river shoals and swamps in three northern districts.