The deal was struck after Whincup sealed his seventh title in Newcastle last November.
"Jamie wanted to wait until the season was done and then it took us about 15 minutes just to finalise that towards the end of last year, put it in the drawer and go on holiday," Dane told Supercars.com.
Whincup added: "I said I’d like to continue driving in 2019, and he said ‘sure, no problems’. That was it.
"We’ll probably have to some paperwork at some stage, but paperwork’s not important, if two blokes agreed on something, the deal’s done in my eyes."