Last month a tribunal heard officers used anti-terror legislation in 2012 to find out the source of damaging leaks.
Announcing a major overhaul of their professional standards department, Iain Spittal said he personally apologised to the Northern Echo journalists.
He said the division needed changing and would face a "thorough review".
The announcement was made along with Police and Crime Commissioner Barry Coppinger.
"There needs to be a fundamental change in how we deal with complaints and how we investigate wrong-doing - and now is the right time to begin the change," Mr Spittal said.
The force will look at how other regulatory bodies operate and its new head could come from outside the police.
Although the findings of the Investigatory Powers Tribunal will not be released until later this month, Mr Spittal said the panel had indicated the use of the Regulation of Investigatory Powers Act (RIPA) was "unlawful".
He said: "Whilst we have not received the final judgment, on behalf of the organisation, I feel it is right to apologise for the use of RIPA in 2012.
"As a result, before Christmas I made contact with the individuals concerned to offer personal apologies to them."
Cleveland Police previously claimed it was justified in using RIPA - which has since been replaced.
The chief constable of Cleveland Police has apologised to two journalists after the force unlawfully accessed their private phone records.