Smith has agreed a new one-year contract after helping keep Wildcats in First Utility Super League.
He took over in May from previous boss James Webster and was in charge for last week’s victory over Bradford Bulls in the million pound match.
Wildcats’ win in a one-off shoot-out secured their top-flight status, after they finished 11 points adrift at the foot of the table.
Smith, 61, had been considering returning to Australia, but Carter said: “I am ecstatic to have got him for next year.
“He is a fantastic bloke to work with and he’s been a breath of fresh air for everyone at the club, from the cleaners to the on-field staff.
“I hope it shows the fans our intentions.
“I don’t think Brian would have done that if we weren’t backing him as a board and club so that shows what we’re intending for 2016.
“He is looking to build the club for the next 10 years, on and off the field and I’m delighted to have got Brian to commit,” he said.
Smith’s decision is a huge boost to Wildcats, who have agreed new deal allowing them to remain at Belle Vue for a reduced rent and hope to be debt-free by the end of the year.
Carter said the club expect to launch next year’s season tickets early this week and with the coach in place, plans for next year’s squad can now move forward. Several of this year’s team are close to agreeing contracts for 2016 and Carter added: “We have got eight or nine new signings lined up, which we hope to be able to confirm soon.”
Smith is one of the most respected coaches in the sport. He had previous spells in England with Hull and Bradford and has coached teams to four Grand Final in Australia.