All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We pray to Allah to help all of us to do what pleases Him and to guide us to the right path.
Dear brother, know that it is not sufficient nor beneficial to discuss the subject of "Islamic state form of government" in a Fatwa or even some papers. Such an issue needs an earnest detailed research. So, we refer you to some books on as-Siyasah ash-Shar'iyah (Administrative and regulative policies in Sharee’ah) and form of government in Islam. Here are some of those books:
(1) as-Siyasah ash-Shar'iyah by Ibn Taymiyyah
(2) al-Turuq al-Hukmiyyah by Ibn al-Qayyim,
(3) al-Ahkam al-Sultania by al-Mawardi,
(4) Ghiyath al-Umam fi Iltayath adh-Dhulam by al-Juwayni.
In general, the nomination of a ruler in Islam is based on Shoorah (mutual consultation).
Allah Says (what means): {…And whose affair is [determined by] consultation among themselves, and from what We have provided them, they spend.…} [Quran 42: 38] Allah also Says (what means): {… So pardon them and ask forgiveness for them and consult them in the matter. …} [Quran 3: 159]
So, Ahlul Hal wal 'Aqd (Influential people, those in power as representatives of the people) meet and consult and then nominate a ruler whom they think is qualified to the position of Khilafah (Caliphate). After that, they pledge allegiance to him and urge the Muslim Ummah to pay homage to him. So, he becomes entitled to manage all affairs, inner and outer, provided that he sticks to the Sharee'ah and never violates its rulings.
Since most affairs of as-Siyasah ash-Shar'iyah are subject to Ijtihad (juristic opinion on matters on which the Quran and the Sunnah has not specified), the ruler can compare between what is good and bad for the Muslim public, and then, choose what is better and more beneficial for the Ummah.
Here, we state that forming a government is based on the principle of “Choosing what is better and more beneficial for the Ummah”. Thus, the Muslim ruler can form the government and choose the best people to be ministers. At the same time, the ruler may deputize Ahlul Hal wal-'Aqd (The Islamic parliament) to form the government. In fact, there are many choices.
Allah knows best.