Barbour and Crick both drove in two rounds with Team Triton last seasons, with the former winning in his second outing at Sandown.
"I am thrilled to be joining Team Triton for the full 2019 championship,” said Barbour.
“After joining the team in a testing role and becoming a fill-in driver in 2018 I was hopeful that after our strong round win at Sandown I would be given the opportunity to do a full year.
“I’m very grateful to Craig, Mitsubishi, and all our partners for putting the faith in me to have a big crack in the #78 this year, and to be able to do it in the new Mitsubishi Triton MY19 is the icing on the cake.
“I can’t wait to get on the streets of Adelaide as I’ve always loved the track and event."