Mr Tamihere sued the media company -- which operates TV3 and a string of radio stations -- in December 2013 alleging defamation and breach of contract.
He said he had been made a scapegoat following a public backlash to an interview with a female caller who claimed to be friends with one of the young men accused of boasting online about their sexual conquests of underage girls.
The case had appeared destined for a lengthy period of litigation until a surprise settlement was agreed on Friday.
Lawyers for MediaWorks had sought to have the case settled by private mediation. In response Mr Tamihere lodged an appeal with the Court of Appeal arguing the case should be heard in an open court.
That action was withdrawn once the two parties a reached a confidential settlement, which includes a commitment by MediaWorks to broadcast an apology before or after a primetime news bulletin.
Mr Tamihere and co-cost of the Willie and JT Show, Willie Jackson, were heavily criticised following a November 2013 interview with a mystery 18-year-old caller known only as Amy.
The interview was interpreted by some as victim blaming and Mr Tamihere and Mr Jackson were both stood down in the face of a threatened boycott by RadioLive advertisers. Mr Jackson later returned to the air with Alison Mau as his co-host, while Mr Tamihere's contract was not renewed.
Mr Tamihere alleged the public had been left with the impression he had acted inappropriately despite the fact an internal MediaWorks investigation had cleared him of breaching any broadcasting standards.
MediaWorks' investigation found Mr Tamihere had acted "entirely within his bounds" as a talkback host and had not breached any standard of good taste and decency.
MediaWorks' apology will state the company "unreservedly apologises for any harm caused to Mr Tamihere's reputation and mana".
No charges were laid over the alleged offending in the Roastbusters scandal. It caused widespread outrage after it was revealed young men were posting videos of themselves online bragging about sexual activities with drunk, underage girls, some as young as 13.
The results of an Independent Police Conduct Authority inquiry made public in March identified a slew of inadequacies in basic policework relating to the case and police issued a public apology to the victims.
