"On this historic occasion and joyous moment of your victory, I wish you and the friendly people of India all the very best," she said adding that "I most warmly invite you, to visit Bangladesh at your earliest convenience."
In a separate letter to BJP President Rajnath Singh, Ms Hasina, chief of the Awami League, said "the magnitude of BJP's victory is clearly reflective of the charismatic leadership quality of yours and the Prime Ministerial Candidate of BJP Shri Narendra Modi, your top office bearers and election campaign strategists and managers, as well as the huge degree of trust and confidence that the people of India have chosen to repose in your Party and in your leadership."
She vowed to work with BJP and the elected government of India to bring about "meaningful, tangible and positive changes in our close and friendly relations". Ms Hasina also invited Mr Singh to visit Bangladesh.
Bangladesh Nationalist Party (BNP) chief and former prime minister Khaleda Zia also congratulated Mr Modi who has led the BJP to a resounding victory in the polls.
"She (Zia) has sent a message of greetings (to Modi) through the Indian high commission in Dhaka," BNP vice chairman and party spokesman Shamser Mobin Chowdhury said.
