As you have asked about the list of approved universities by All India Council for Technical Education (AICTE) offering distance education programs, I am mentioning some of them, check below for the details

Acharya Nagarjuna University, Guntur
Andhra University, Visakhapatnam
Dr. B.R. Ambedkar Open University, Hyderabad
Dravidian University, Kuppam
Gitam University, Visakhapatnam
Jawaharlal Nehru Technological University, Hyderabad
Kakatiya University, Warangal
Maulana Azad National Urdu University, Hyderabad
NALSAR University of Law, Hyderabad
Osmania University, Hyderabad
Potti Sreeramulu Telugu University, Hyderabad
Rashtriya Sanskrit Vidyapeetha, Tirupati
Rayalseema University, Kurnool
Sri Krishnadevaraya University, Anantapur
Sri Padmavati Mahila Visvavidyalayam, Tirupati
Sri Venkateswara University, Tirupati
University of English & Foreign Languages, Hyderabad
University of Hyderabad, Hyderabad
ICFAI Foundation for Higher Education, Hyderabad
National Institute of Rural Development, Hyderabad
Dr. B.R.Ambedkar Open University, Hyderabad
Dr. Babasaheb Ambedkar Open University, Ahmedabad, Gujarat
Karnataka State Open University, Mysore, Karnataka
Aligarh Muslim University, Aligarh
Allahabad Agricultural Institute (Deemed University), Allahabad
Amity University, Noida
Dayalbagh Education Institute, Agra
Dr. B.R. Ambedkar University, Agra
Jagatguru Ram Bhadracharya Handicapped University, Chitrakoot Dham
Shobhit Institute of Engg. & Tech. (Deemed University), Meerut
University of Allahabad, Allahabad
University of Lucknow, Lucknow
Krishanakant Handique State Open University, Guwahati, Assam
M.P.Bhoj(Open) University, Bhopal, MP
Nalanda Open University, Patna, Bihar
Netaji Subhas Open University, Kolkata, WB
Pt. Sunderlal Sharma (Open) University, Bilaspur, Chattisgarh
Tamil Nadu Open University, Chennai, Tamil Nadu
U.P.Rajarshi Tandon Open University, Allahabad, UP