The ministers and 42 assistant ministers were immediately sworn into office before President Abd Allah Yusuf Ahmad in Nairobi on Friday.
Gadi said he made a slight change to his first cabinet, which was sacked on 11 December, in order to respect the principle of equal distribution of power among five major clans and one minor in Somalia, as envisaged by the country's transitional constitution.
The new team is expected to fill a 13-year power vacuum in the state, which first descended into chaos in 1991 when Muhammad Siad Barre was toppled.
"I have made this list to the best of my ability," Gadi told his new ministers.
"Those given posts will have a task of serving Somalia [at] a critical point ... some [of you are] unhappy because they were not in the list of the cabinet, but hopefully tomorrow, they will be in the list. This is not a permanent cabinet," Yusuf said.
When the first government was formed on 1 December, some tribal leaders were not happy with the posts they were allocated.
All of the Somali officials involved in efforts to set up a new government, including Gadi and President Yusuf Ahmad, are based in the Kenyan capital, Nairobi, because their own, Mogadishu, is still considered too dangerous.
"The cabinet should immediately draw a timetable for the relocation of our government. We should go and serve the people of Somalia immediately, not sit here in Kenya," he added.
Since 1991, two governments have been formed, but neither managed to establish control across the country, where rival chiefs have wreaked havoc and carved themselves fiefdoms.
Hope for success is much higher in this round of peace talks, which started in Kenya in 2002, mainly because previously excluded tribal chiefs were brought into the negotiations.