Can we trust Plod?
The broadcaster says the apology and the promise of £100,000 will be made at the High Court on Thursday.
It follows comments made about a Dispatches programme, Undercover Mosque, which tackled claims of Islamic extremism in the West Midlands.
A police spokeswoman confirmed an apology would be read out in court.
A press release issued by the police and the CPS in August 2007 claimed the Dispatches programme, broadcast in January of that year, misrepresented the views of Muslim preachers and clerics with misleading editing.
Channel 4 was fully aware of the sensitivities surrounding the subject matter but recognised the programme's findings were clearly a matter of important public interest
One preacher was shown saying a homosexual should be thrown off a mountain, another that women were born deficient.
Police also reported Channel 4 to television watchdog Ofcom for "heavily editing" the words of Islamic imams.
But in November, Ofcom rejected the police and CPS claims, and Channel 4 said it was going to sue the CPS and police for libel.
Kevin Sutcliffe, deputy head of current affairs at Channel 4, said the apology was a vindication of the programme team in exposing extreme views.
"Channel 4 was fully aware of the sensitivities surrounding the subject matter but recognised the programme's findings were clearly a matter of important public interest.
"The authorities should be doing all they can to encourage investigations like this, not attempting to publicly rubbish them for reasons they have never properly explained," he said.
David Henshaw, executive producer of Hardcash Productions, who made the documentary, said it was a thorough and detailed programme, made over nine months and at personal risk to the undercover reporter.
The programme infiltrated a number of mosques, one of which was Green Lane Mosque in Small Heath, Birmingham.
An undercover reporter claimed to provide evidence that certain speakers preached messages of religious bigotry and extremism."
PC used to stand for Police Constable. Now it is for Politically Correct. Criticise minorities, especially followers of "The Religion of Preace" or homosexuality and your collar will be felt. It is a sad day when journalists are more trustworthy than those entrusted with law enforcement.