Prime Minister Tony Blair has defended splitting up the Home Office, saying it "makes sense" to allow the department to focus on terrorism.
A new Justice Ministry has taken on responsibility for prisons, probation and sentencing from the Home Office.
Critics say the split will compound the existing problems and create new ones.
But Mr Blair told MPs on that it was sensible to have one department controlling prisons, probation and courts, as other countries did.
The new Ministry of Justice, which starts operating from Wednesday, will take on responsibility for prisons, probation and sentencing, while the Home Office will keep responsibility for security, crime, drugs, counter-terrorism and ID cards.
'Last thing needed'
Mr Blair was responding to criticism from Tory leader David Cameron, who said: "The last thing a department in crisis needs is the huge distraction of a big reorganisation."
In a reference to John Reid, who has said he will step down as home secretary when Mr Blair resigns, Mr Cameron added: "If splitting the Home Office is such a good idea - why isn't the home secretary hanging around to see it through?"
Mr Blair replied that a Tory proposal to have a separate counter terrorism Cabinet minister in the Home Office was "very foolish" and it was important to allow the Home Office to focus on fighting terrorism.
He added: "I believe it's right to take the prisons and probation out of the Home Office and into a new ministry of justice."
Judges have expressed concern that courts and prisons will share a budget and they may have to choose between losing staff or passing shorter sentences.
In a statement, the Lord Chief Justice Lord Phillips - the top judge in England and Wales - said "full agreement" had yet to be reached with the government. He said a special meeting of the Judges' Council would be staged next Tuesday to discuss the situation.
Bar Council chairman Geoffrey Vos QC also raised concerns, saying legal aid should be made a high priority and the funding of the judiciary must not depend "in any way on the crises affecting the prison system".
But Lord Falconer, who will head up the new Ministry of Justice, told the BBC it would mean a better justice system with less re-offending, better public protection and more effective sentencing.
HOME OFFICE SPLIT
Two ministries instead of one
Home Office to refocus on security, policing, counter-terrorism, immigration, borders and ID cards
Ministry of justice for courts, prisons, sentencing policy, probation
"I believe it is the right thing to do," said Lord Falconer - who also retains his old role as Lord Chancellor.
"There are concerns about how the money will be split up between courts and prisons and we are discussing with the judges how safeguards can be put in place.
"But that shouldn't detract from the sole purpose of doing it, which is to get better outcomes from the justice system in favour of the public."
The changes come a year after Mr Reid took over as home secretary, saying the department was "not fit for purpose" following a series of controversies over immigration failures and the failure to consider more than 1,000 foreign prisoners for deportation.
One of the issues facing the ministry will be prison overcrowding in England and Wales, where a record number of people - more than 80,300 - are being held.
The Ministry of Justice will have seven ministers - including the existing Department for Constitutional Affairs team, Gerry Sutcliffe who is transferring from the Home Office and a new post has been created for former Northern Ireland minister David Hanson.
The Home Office will have six ministers - the first time it has had fewer than the DCA.