Dr Singh, who was forced by the Trinamool Congress chief to remove Mr Trivedi from the Cabinet after he proposed rail fare hike in the budget, said a new Railway Minister will be sworn in soon.
"I received late last night an email message followed by a formal letter from Dinesh Trivedi tendering his resignation as Railway Minister," the Prime Minister told the Lok Sabha while replying to the debate on Motion of Thanks to the President's Address.
He said he would forward the letter to the President with the recommendation to accept the resignation.
"I regret the departure of Shri Trivedi," he observed.
Dr Singh said Mr Trivedi had "presented a Railway Budget that had promised to carry out the Vision 2020 outlined by his predecessor," a reference to Ms Banerjee.
Ms Banerjee had outlined Vision 2020 two years ago as a blueprint for modernising the railways.
"A new railway minister will be sworn in shortly. He will have the onerous duty of carrying forward the challenging task of modernising our railway system," Dr Singh said.