In a letter to Mukherjee, Singh recalled that he and his cabinet colleagues had benefitted from his "wise counsel" on innumerable occasions and will "deeply miss" his presence.
"Our government owes a deep debt of gratitude to you for your invaluable contribution to its work over the last eight years," he said.
"It is a testimony to your extraordinary abilities and your stature in public life that you have carried on onerous range of responsibilities with ease and accomplishment," Singh said.
"Our colleagues in the cabinet and I have benefitted from your wise counsel on innumerable occasions and we will all deeply miss your presence amidst us," the Prime Minister said.
Singh said he hoped to see Mukherjee occupy the exalted position of the President next month and was confident that "the country and the people will continue to benefit from his wisdom, knowledge and decades of experience in public life".
"I wish you success in the election to the highest office in the country. I also wish you sustained good health and happiness in the years to come," he said.
The Prime Minister also informed Mukherjee that he has forwarded his letter of resignation from the Cabinet to the President with a request that it be accepted with immediate effect.
