The government led by Prime Minister Benjamin Netanyahu was sworn in late on Thursday after winning a narrow approval by parliament.
Aryeh Deri, the new economy minister and head of the ultra-Orthodox Shas party, spent 23 months in prison after he was convicted in 2000 of taking $155,000 in bribes during his term as interior minister.
Incoming Justice Minister Ayelet Shaked, of the far-right Jewish Home party, has been raising hackles during her past two years as a member of parliament.
In a posting on her Facebook page last summer she endorsed an article written in 2002 by then settler leader Uri Elitzur which labelled Palestinian militants as "snakes", described "the entire Palestinian people (as) the enemy" and said anyone supporting terror should be killed.
Former general Yoav Galant, appointed as armed forces chief in 2010 was disqualified before he could take office, over allegations that he had illegally grabbed public land around a luxury villa he built, and lied when questioned about it.
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With magnificent irony, Galant, number two in the centre-right Kulanu party, now becomes minister of construction and housing.
The ultra-Orthodox United Torah Judaism was one of the first parties to sign up to Netanyahu's coalition but has no portfolios.
Its members, who have theological misgivings about swearing allegiance to the secular Zionist state, get around the problem by serving as deputy ministers or heads of powerful parliamentary committees.
In Netanyahu's new government, party members will hold the positions of deputy minister of health and chair of the house finance committee.
The ultra-Orthodox also have a prohibition on shaking hands with members of the opposite sex, but deputy foreign minister Tzipi Hotovely, an ultra-Orthodox woman from the Likud's far right made a point of issuing a statement saying she would not offend foreign officials by refusing any proffered hands, the top-selling Yediot Aharanot newspaper reported on Friday.
"She intends to abide by the religious ruling that states that if a man extends his hand to a woman, it is customary to shake it so as not to embarrass him," it said.