Sunni Arabs have little voice in the current cabinet, which is dominated by Shia and ethnic Kurds.
Four independent candidates will also replace those from the bloc of Muqtada al-Sadr, which has boycotted the government since last year.
Salim al-Jubouri, a member of the front, said after the vote: "Today, parliament voted to accept our candidates ... This means the Accordance Front has officially returned to the government.
"It is a real step forward for political reform."
Al-Jubouri, who is also the bloc's spokesman, said the front's approved candidates would attend the next cabinet meeting.
Political posts
The ministers include Rafie al-Issawi, who was voted in as the Sunni deputy prime minister. He was previously minister of state for foreign affairs between 2005 and 2007.
Sunnis will also take the higher education, culture and communications, foreign affairs, and women's affairs portfolios.
The four independents will take the posts for transport, tourism, provincial affairs and civil society.
The front pulled out of al-Maliki's cabinet in August last year, demanding a greater say in security policies as well as the release of Sunni Arab detainees who make up the bulk of detainees. Most of its cabinet seats were never filled.
A senior US official said: "After some dithering ... [the front] very quickly rallied around the prime minister, post Basra. There's a new and more welcome spirit of unity."
Knock-on effect
The political rapprochement has also been a factor in improved ties between Iraq and Sunni Arab states.
Until recently, Arab capitals maintained only low-level ties with the country partly because they believed the Sunni Arabs were victims of sectarian policies in Iraq.
In March this year, al-Maliki launched a series of crackdowns against Shia militias starting in the southern oil city of Basra. He had previously been accused of ignoring sectarian violence against Sunnis carried out by groups such as the al-Mahdi Army, which swears allegiance to al-Sadr.
Sadrists continue to boycott the government, and the Sunnis would appear to have lost the planning ministry to the Shia after they expelled Ali Babban, the minister who refused to keep last year's boycott and rejoined the cabinet.