Mr McCaffrey and Mr Birney were arrested over the alleged theft of a police watchdog document that appeared in their film No Stone Unturned about a notorious loyalist massacre in Loughinisland, Co Down in 1994, during the Northern Ireland Troubles.
The investigation into the documentary makers was later dropped.
Mr Byrne sent separate letters to the men on Thursday.
In the letter to Mr Birney, he wrote: “I am writing to you on behalf of the Police Service of Northern Ireland to place on record my unreserved apology to you and your family for the distress and upset caused by the execution of search warrants at your home and business premises on 31 August 2018.”
“While the searches were planned and conducted at the direction of officers from Durham Constabulary, those officers were acting on behalf of the Police Service of Northern Ireland in an external capacity and I fully accept the ruling of the Lord Chief Justice that the search warrants were unlawful.”
He said the PSNI would be reviewing the findings of the judgment “to ensure that all appropriate learning is taken”.
Mr Byrne said: “I have notified both Mr McCaffrey and Mr Birney’s legal representatives that I am keen to resolve all the outstanding matters through a process of mediation in order to bring this matter to a conclusion.”