The keeper joined from Sparta Prague on loan for the second half of the season, and he has impressed manager Rafa Benitez.
Now the Magpies are going to seal the transfer when the window opens in the summer. The deal should keep Dubravka at the club for the next few years.
Sky Sports claim that Newcastle also want to sign Chelsea's youngster Kenedy on a permanent deal, after his successful loan spell. But that deal is more difficult, as Chelsea are not keen to lose the talented winger just yet.