Finance Minister Nick Minchin will become Senate leader with Communications Minister Helen Coonan as his deputy.
However Mr Howard refused to be drawn on whether he would lead his new-look government into the next election, due in 2007, despite widespread speculation that he could step aside in favour of Treasurer Peter Costello, whose ambitions for the top job are widely known.
Mr Hill is expected to be named as Australia's next ambassador to the United Nations, after he resigned last week.
While Mr Howard described the cabinet changes as "significant", most senior ministers will retain their posts apart from the defence portfolio.
Ageing Minister Julie Bishop will take over from Mr Nelson as Education Minister, and Ms Bishop will be replaced by Queensland senator Santo Santoro.
Indigenous affairs would be taken out of Immigration Minister Amanda Vanstone's portfolio and given to assistant treasurer Mal Brough, who also replaces Kay Patterson as Family and Community Services Minister.
Ms Patterson resigned on Sunday, and Fisheries and Conservation Minister Ian Macdonald also announced that Mr Howard had told him he would be dumped.
Labor's foreign affairs spokesman Kevin Rudd said ahead of the reshuffle that Howard was sweeping out moderates to form a far-right ministry.
"What becomes clear through this reshuffle is that Howard is desperately protecting his own incompetent supporters, such as (Foreign Minister) Alexander Downer, and at the same time launching a purge of Liberal moderates," he said.
All three ministers "forced out" were moderates and supporters of Costello, Mr Rudd said.
New-look cabinet:
Cabinet
Prime Minister: John Howard
Trade and Deputy Prime Minister: Mark Vaile
Treasury: Peter Costello
Foreign Affairs: Alexander Downer
Attorney-General: Philip Ruddock
Finance and government leader in the Senate: Nick Minchin
Communications: Helen Coonan
Health: Tony Abbott
Families, Community Services and Indigenous Affairs: Mal Brough
Defence: Brendan Nelson
Education, Science and Training, assisting prime minister on Women's issues: Julie Bishop
Immigration and Multicultural Affairs: Amanda Vanstone
Agriculture: Peter McGauran
Employment and Workplace Relations: Kevin Andrews
Transport and Regional Services: Warren Truss
Environment and Heritage: Ian Campbell
Industry, Tourism and Resources: Ian Macfarlane
Outer ministry
Local Government, Territories and Roads: Jim Lloyd
Arts and Sport: Rod Kemp
Human Services: Joe Hockey
Small Business and Tourism: Fran Bailey
Veterans' Affairs: Bruce Billson
Ageing: Santo Santoro
Community Services: John Cobb
Assistant Treasurer and Revenue: Peter Dutton
Workforce Participation: Sharman Stone
Fisheries, Forestry and Conservation: Eric Abetz
Special Minister of State: Gary Nairn
Vocational and Technical Education: Gary Hardgrave
Justice and Customs: Chris Ellison
Parliamentary secretaries:
Malcolm Turnbull (to the prime minister and water policy)
Andrew Robb (to immigration and multicultural affairs)
Teresa Gambaro (to foreign affairs)
Richard Colbeck (to finance and administration)
Sussan Ley (to agriculture, fisheries and forestry)
Sandy Macdonald (to defence)
Bob Baldwin (to industry, tourism and resources)
De-Anne Kelly (to trade)
Pat Farmer (to education)
Greg Hunt (to environment)
Christopher Pyne (to health)
Chris Pearce (to the treasurer)