State Liberal president Rod Scurrah said he had no doubt Mr Gutwein will be a great premier.
“Along with continuing Deputy Premier Jeremy Rockliff, Peter has been an integral part of the leadership team of the Tasmanian Liberal Party since his election in 2002,” he said in a statement.
Mr Gutwein and Mr Ferguson were vying for the top job in what was seen as a contest between the party’s moderate and conservative factions.
Mr Ferguson had planned on running with Attorney-General Elise Archer as his deputy, but pulled out of the race on Monday morning after spending the weekend talking to colleagues.
“As I said last Thursday, my position, as always, is to do what is best for our party, the government and most importantly the Tasmanian people,” he said.
“Peter Gutwein and Jeremy Rockliff have made significant contributions to Tasmania in their Parliamentary careers and they will be a strong and dependable leadership team. We respect them. They will have our full support.”
Mr Gutwein represents the moderate faction of the party, with devout Christian Mr Ferguson the more conservative option.
Mr Hodgman last Tuesday stepped down as premier after six years in the role and 18 years in politics, citing a desire to spend more time with family.
He said a mid-term exit was the right time for fresh leadership ahead of the next state poll in 2022.