"There are still further tests to be done to figure out where to go from here, but so far it was gone really well."
Baxter added that the team was "relieved" with the news.
"It has been pretty hard to be on-air laughing and talking about stuff when we know our best friend is in a really tough spot."
Simon and Jodi have been married for more than 25 years and have four children together, Sammy, Sophie, Bella, and Lily.
"She is utterly and completely my soulmate," he told Woman's Day in 2015, shortly after winning Dancing With the Stars.
"We don't feel complete unless we are together."
Barnett is set to join Newstalk ZB early next year.