They put in their papers late Sunday night following directions from the Congress central leadership, party sources said.
However, an official confirmation of the resignations is expected later Monday. The chief minister is likely to forward the resignations of both the ministers to governor ESL Narasimhan for acceptance.
Home Minister P Sabita Indra Reddy and Roads and Buildings Minister Dharmana Prasada Rao met Kiran Kumar Reddy at the latter's residence here around midnight.
Both the ministers later switched off their mobiles but left for their respective homes in their private vehicles after surrendering their official vehicles, giving credence to the buzz about their resignations.
The ministers submitted their resignations hours before Telugu Desam Party (TDP) chief N Chandrababu Naidu is scheduled to meet President Pranab Mukherjee in New Delhi to demand sacking of the tainted ministers.
The Congress leadership had made it clear on Saturday that the ministers should voluntarily resign. The direction came after the chief minister camped in Delhi for four days, holding talks with the key leaders.
After his return to Hyderabad, the chief minister summoned Dharmana, who was in his native Srikakulam district in north coastal Andhra, 600 km from here. Sabitha, the first woman to become home minister in the state's history, hails from Ranga Reddy district abutting Hyderabad.
After he was named as an accused in the fourth chargesheet filed by the Central Bureau of Investigation (CBI) in August last year, Dharmana had submitted his resignation but it was not accepted by the chief minister, who also refused to give permission to the Central Bureau of Investigation to prosecute him.
Sabitha had also offered to quit after she was named in the fifth chargesheet filed last month but the chief minister advised her not to do so.
Both the ministers, who had served in the cabinet of Jaganmohan Reddy's father YS Rajasekhara Reddy (2004-09), have been accused of showing undue favours to companies which invested in Jaganmohan Reddy's business.
Sabitha served as mining minister in YSR's first cabinet while Dharmana held revenue portfolio.
In May last year, then excise minister Mopidevi Venkatramna had resigned after he was arrested by the CBI in the same case. He was minister for infrastructure and investment in YSR cabinet.
However, three other ministers who were also issued notices by the Supreme Court last year in connection with the controversial orders issued by them, were left untouched.
The demand for dropping the tainted ministers gathered momentum after two central ministers, Ashwini Kumar and Pawan Kumar Bansal, resigned recently on the direction of Congress leadership in view of certain allegations against them.