Prime Minister Haider al-Abadi's programme was pushed through without debate, according to parliamentary speaker Salim al-Juburi.
Under the plan, Mr Abadi will cut spending and eliminate senior posts.
It follows recent anti-government protests over an unreliable electricity supply amid a major heatwave.
Thousands of people have turned out in Baghdad and other cities to vent their anger at the authorities and pressurise them to make changes.
Iraq's system of sharing government jobs has long been criticised for promoting unqualified candidates and encouraging corruption.
The country has three vice-presidents - two from the Shia Muslim majority and one from the Sunni Muslim minority - and three deputy prime ministers - a Shia, a Sunni and a Kurd (also a Sunni).
As a result of the reforms, senior political appointments will no longer be based on sectarian or party quotas, and the posts of vice-president and deputy PM will be abolished.
Mr Abadi's seven-point plan also includes a requirement for a number of government positions to be filled with political independents - a move aimed at cracking down on corruption.
Officials' benefits will also be reduced.
The changes come after weeks of protests by voters angry at the way the country is governed and at the lack of investment in infrastructure.
In some areas of Iraq it is common to have only a few hours of electricity each day.
Tensions have become particularly fraught during a heatwave that has seen temperatures rise to 51C (123F).
Frequent power cuts have made the sweltering conditions even more unbearable.
Many Iraqis have cautiously welcomed the passing of the reform package, seen as a victory for Mr Abadi.
But he still faces pressure to ensure the measures are properly implemented.
Mr Juburi said a complementary plan containing even more reforms was needed, and called on Mr Abadi to sack ministers who were guilty of negligence and corruption.

Winger Young won the last of his 30 caps against Ukraine in September 2013.
But his form under Van Gaal has led to suggestions England coach Roy Hodgson might end that exile when he names his squad on 19 March for the games against Lithuania and Italy.
"The manager has been fantastic," said Young. "He gives you the confidence to play and confidence helps massively."
He added:  "I can only repay him with my performances on the pitch. That is what I have shown this season."
Young has been used as a full-back and at wing-back this season.
Van Gaal picked the 29-year-old former Watford and Aston Villa player in a more orthodox wide position in the 3-0 win over Tottenham.
Hodgson was at Old Trafford to watch one of United's best performances of the season - and a player who was an ever present at Euro 2012.
"Fingers crossed I can get myself back into the England team," said Young, speaking at a bwin event.
"I have always said I want to represent my country. It is an honour to play for England and hopefully I have done enough to get myself back into the squad.
"But I am concentrating on events at my club and we will just have to wait and see."

Englishwoman Evans, 29, is a 10-time ladies' champion.
Doherty, 45, won the tournament in 1997, but the world number 43 has not reached the third round since 2006.
The winner must make it through two more qualifying rounds to reach the main draw, which starts on 18 April.
The tournament has increased this year from 128 to 144 players. The top 16 seeds automatically qualify for the first round, with all non-seeded players starting in the first of three qualifying rounds which run from 8-15 April.
Evans received an invitation to the qualifying draw from snooker's governing body, the World Professional Billiards and Snooker Association (WPBSA).
Six-time world champion Steve Davis is also attempting to qualify. He faces Jamie Cope in the first round of qualifying.
Jimmy White, six times a runner-up at the Crucible, meets Thailand's James Wattana, while 2006 world champion Graeme Dott has been drawn against Mark Owens.
Defending champion Mark Selby is the top seed, with five-time winner Ronnie O'Sullivan seeded second - the two met in last year's final.
The Iraqi parliament has unanimously approved reforms aimed at stamping out corruption, reducing government waste and easing sectarian tensions.
[NEXT_CONCEPT]
Ashley Young says Manchester United manager Louis van Gaal has helped revive his hopes of an England recall.
[NEXT_CONCEPT]
Reanne Evans will face former world champion Ken Doherty in the first round of qualifying as she bids to become the first woman to appear in the main stages of the World Championship.