This list is taken from a BBC World Monitoring translation of Sharq, an Iranian Reformist Newspaper. This appeared in the 22 June, 2013 publication of Sharq, and was translated by the BBC World Monitoring service on 24 June, 2013.
What is striking about this list is the number of reformists and members with connections to Rafsanjani. (There may be more connections that I am unaware of, but most of these people are unknown outside Iran so it is hard to know for certain).
Former members of Khatami's government are highlighted in red, former members of Rafsanjani's government are highlighted in blue, former members of both are purple, former members of Mousavi's are green
First vice-president: Mohammad Reza Aref—Reformist presidential candidate from the 1392/2013 election, and former First vice-president under Khatami
Secretary of Supreme National Security Council: Ali Akbar Velayati—Presidential candidate from 1392/2013
Ministry of Education and Training: Ali Motahhari— Son of assassinated protegĂ© of Ayatollah Khomeini, Morteza Motahhari
Ministry of Economic and Financial Affairs: Mohammad Baqer Nobakht
Foreign Ministry: Mahmoud Va'ezi
Ministry of Health Care and Medical Education: Mas'ud Pezeshkian—Held same position under Khatami
Ministry of Agricultural Jihad: Esa Kalantari—Same position under Rafsanjani
Ministry of Justice: Hojjat ol-Eslam Shushtari— Same position under Rafsanjani and Khatami
Ministry of Defense and Armed Forces Logistics: Akbar Torkan— Same position under Rafsanjani (Minister of Roads in Rafsanjani's 2nd term)
Ministry of Roads and Urban Development: Ali Abdol'alizadeh
Ministry of Industries, Mines and Commerce: Mohammad Reza Nehavandian
Ministry of Science, Research and Technology: Ja'far Tawfiqi—Same position under Khatami
Ministry of Culture and Islamic Guidance: Mohammad Ali Zam
Ministry of Labor and Cooperatives: Morteza Bank—Deputy Foreign Minister under Khatami
Ministry of the Interior: Hojjat ol-Eslam Ali Akbar Nateq-Nuri—Same position under Mousavi
Ministry of Oil: Bizhan Namdar Zanganeh— Minister of Jihad?? under Rafsanjani and Khatami
Ministry of Energy: Habibollah Bitaraf— Same position under Khatami
Ministry of Sports and Youth Affairs: Mohammad Fard
Plan and Budget Organization: Mohammad Ali Najafi—Same position under Khatami (Minister of education under Rafsanjani)
Atomic Energy Organization: Gholamreza Aqazadeh
Ministry of Communications and Information Technology: Ahmad Mo'tamedi
Vice-president for Majles affairs: Qodratollah Alikhani
Environmental Protection Organization: Ma'sumeh Ebtekar—Same position under Khatami (first female leader in this role)
Central Bank: Majid Qasemi
Vice-president of the republic and chief of the Martyr Foundation: Hoseyn Dehqan
Vice-president of the republic for clerical affairs: Hojjat ol-Eslam Shahidi
Vice-president for technology: Alireza Olfat—Member of Khatami's govt
Government Secretary and Spokesman: Alireza Nateqi—Chairman of Rouhani's Campaign Committee
Ministry of Information: Ali Younesi—Same position under Khatami
Chief of the President of the Republic's Center for Women's Participation and Family Affairs: Zahra Pishgahifard—Female
Ministry of Intelligence: Ali Younesi—Same position under Khatami (unsure if same as Information Ministry)
Chief of Cultural Heritage and Handicraft Industries Organization: Hoseyn Mar'ashi
Consultant to the president of the republic and supervisor of the Presidency Institute: Mohammad Reza Ne'matzadeh—Minister of Labor under Rafsanjani
Consultants to the president of the republic: Dr. Mohammad Reza Sadeq, Ali Asgari, Hoseyn Faridun (Rouhani's brother)
Special inspector for the president of the republic: Hoseyn Faridun (Rouhani's brother)
UPDATE 1:
American Enterprise Institute published a list on 19 June based on a report from Tasnim (a principlist paper). There are some differences and some similarities, but the list is far less complete and only has a few names.
E'tedad (A reformist paper) on 20 June
published an analysis with similar names. Because of the consensus between several papers with different political leanings, I feel as though its safe to say that Ali Younesi and Mouhammad Reza Ne'matzadeh are both expected to play important roles in Rouhani's government. There are some significant differences between the
E'tedad and
Sharq lists, though they have virtually all of the same names.
UPDATE 2:
Al-Monitor has weighed in with some similar opinions although the man they believe will be the next Defense Minister (Shamakhani) is someone not mentioned by
E'tedad or
Sharq (AEI concurs with Al-Monitor on this selection).
UPDATE 3: Another
translated text via BBC Monitoring with more of the same names, although this one also includes the figures appointed to the committee selecting/advising selection of the cabinet. These include:
Yunesi, Torkan, Ne'matzadeh, Hoseyn Rouhani (Faridun), Vaezi, Najafi, Jahangiri, Sadegh, Ashena.
UPDATE 4: CSM picked up a Reuters story quoting Rouhani on his cabinet. Rouhani stated that the cabinet will be inclusive and moderate. This is encouraging to conservatives who may have felt as though they would be excluded, and goes along with the information from UPDATE 3 which states that the reformists wish to keep some of their representatives in the Majles rather than promote them to the cabinet to insure that their seats will remain in the hands of reformists.