Mr Malkinson, now aged 57, spent 17 years in prison after being convicted of raping a woman from Kearsley in Little Hulton in 2003.
But he had his 2003 conviction quashed by the Court of Appeal in July after new DNA evidence potentially linking another man to the crime was identified.
Alex Chalk, the Justice Secretary said the case was “an atrocious miscarriage of justice” as he announced a non-statutory inquiry into Mr Malkinson’s case.
Non-statutory inquiries do not have the legal power to compel witnesses to attend, instead relying on the co-operation of people and organisations involved.
The probe will investigate the handling and the role of Greater Manchester Police, the Crown Prosecution Service and the Criminal Cases Review Commission in his conviction and subsequent appeals to ensure lessons are learned.
Mr Chalk went on: “The core function of our justice system is to convict the guilty and ensure the innocent walk free. Yet a man spent 17 years in prison for a crime he did not commit while a rapist remained on the loose.
“It is essential that lessons are learned in full.”
Mr Malkinson welcomed the news, and said: “I spent over 17 years wrongly imprisoned and so I hope that my lawyers and I will be given the opportunity to feed into the inquiry’s terms of reference.”
“I had to take the police to court twice to force them to hand over evidence.
“The CCRC (Criminal Cases Review Commission) has so far refused to apologise and take accountability. So, naturally, I am concerned that witnesses from these agencies may not co-operate and hand over all the evidence.”
He added: “If there is any obstruction by the agencies involved, then the inquiry needs to be made statutory so that they can be compelled to hand over evidence.
“I want to see serious, profound changes in our justice system coming out of this. My case shows that the police cannot be trusted to investigate impartially or act as faithful gatekeepers to the evidence.
“It also shows that the CCRC, which could have spared me years of life behind bars, is not fit for purpose.”
Mr Malkinson’s solicitor, Emily Bolton, the founder of law charity Appeal, insisted her client “must be at the heart of any inquiry including having a voice in setting its terms of reference”.
She also said the inquiry should be put on a statutory footing “if the agencies involved refuse to act with full transparency and candour”.
A chair will be appointed in due course, as will the publication of the inquiry’s terms of reference, according to the Government.
The Ministry of Justice said Mr Malkinson’s views and experiences will be heard throughout the process.
Case files obtained by 57-year-old Mr Malkinson as he battled to be freed show that police and prosecutors knew forensic testing in 2007 had identified a searchable male DNA profile on the rape victim’s vest top that did not match his own.
No match was found on the police database at the time and no further action was taken.
Mr Malkinson wrote to the CCRC in 2009 for a review of his case, but at the conclusion of its review in 2012, the commission refused to order further forensic testing or refer the case for appeal.
CCRC documents relating to the case between 2009 and 2012 suggest there were concerns about costs.
Responding to the inquiry announcement, Chief Constable Stephen Watson, of Greater Manchester Police, said the force’s participation in the probe would be “fulsome and reflective of integrity, candour and humility”.
He added: “I am very sorry that Mr Malkinson has suffered so grievously over these past many years. I acknowledge and regret the very difficult and prolonged journey that Mr Malkinson has had to undertake to prove his innocence. This appalling miscarriage of justice merits the most detailed scrutiny.”
Helen Pitcher OBE, chair of the CCRC said: “To understand what went wrong in this appalling miscarriage of justice, every organisation involved in handling the case has to fully embrace this whole-system review quite rightly commissioned by the Lord Chancellor (the Justice Secretary).
“We must all contribute fully and engage promptly – and with a commitment to implement any recommendations it draws.”