A party source told : "Rawatji has stepped down from the post of General Secretary and as the (party) in-charge of Assam."
It is the first resignation by any General Secretary after Gandhi's resignation.
Earlier, Rahul Gandhi's sister and Congress General Secretary Priyanka Gandhi hailed her brother saying only "few have the courage that you do".
Rahul Gandhi on Wednesday posted an open letter on Twitter saying he had resigned as "accountability is critical" for the future growth of the party in the wake of the disastrous Lok Sabha election outcome.
"Few have the courage that you do Rahul Gandhi. Deepest respect for your decision," tweeted Priyanka Gandhi.
Congress Treasurer and Rajya Sabha member Ahmed Patel described Rahul Gandhi's resignation as unfortunate and said "he is and will remain his leader".
"Rahulji's resignation letter is unfortunate. We all are accountable for this defeat. He has, in a short span, already made tremendous contribution in strengthening the party and we all believe his endeavour should continue," Patel tweeted.
"He is and will remain my leader, our leader and will continue to provide solid strength for the Congress," he said.
Rahul Gandhi had first told the Congress Working Committee about his decision to quit on May 25, two days after Prime Minister Narendra Modi returned to power and the Congress won only 52 seats in the Lok Sabha.
( With inputs from IANS )