He had initially also sought a retraction of Dr Norman's comment that Mr Craig thought "a gay man's place is in the closet", but he later narrowed the scope of his case.
The comments were made by Dr Norman during a speech at the Auckland festival in February.
Mr Craig had not sought damages, and each party would cover their own costs, the joint statement said.
Both Mr Craig and Dr Norman sought donations from supporters to cover their legal fees.
Dr Norman expected his fees to be around $75,000 if the case went to court. If was not known how much he raised through his public appeal.
At last count, Mr Craig had raised around $50,000 for his cause.
Mr Craig had initially wanted the case to be fast-tracked so it could be resolved before the general election.
His party won 3.97 per cent of the party vote in the election, but failed to win a seat.