Labor leader Rebecca White said Mr Gutwein needed to change course and stop budget cuts to services.

Ms White said the new Premier needed to focus first and foremost on the challenges facing the health system, housings stress and unemployment.

"My concern is the new Premier will be too distracted looking over his shoulder, trying to figure out where Michael Ferguson is, to tackle some of these challenges," Ms White said.

"I'm sure we haven't seen the last of Michael Ferguson's leadership ambitions."

Greens leader Cassy O'Connor congratulated Mr Gutwein on his election but said he had a big job ahead of him.

"He has demonstrated throughout his political career he is capable of change. He needs to change course for the Tasmanian government," Ms O'Connor said.

"We need to see a new Peter Gutwein. Less of the brawler we see in Parliament, more of the statesman and someone who is prepared to make the changes Tasmania needs in this critical decade."

Ms O'Connor said the new Premier needed to focus on the climate emergency, move away from the privatisation of parks and other public assets, rethink his approach to poker machines and improve transparency.

Tasmanian Liberal senator Eric Abetz was the first to extend his congratulations to the new Premier, issuing a media statement just 11 minutes after Mr Gutwein's rival for the top job Infrastructure Minister Michael Ferguson announced he had pulled out of the race.

Liberal Party of Tasmania state president Rod Scurrah said Mr Gutwein would step up and be a great Premier.

Tasmanian Liberal senator Richard Colbeck said both Mr Gutwein and Deputy Premier Jeremy Rockliff had showcased a wealth of political experience and determination to ensure the state continued on a pathway of stability and prosperity.

"Having presided over the state's steady economic growth during the last six years as Treasurer, Tasmanians can be assured of a secure future in Mr Gutwein as leader," Senator Colbeck said.

Bass Liberal MHR Bridget Archer said Mr Gutwein had been a fighter for northern Tasmania since the 2014 election.

"Northern Tasmanians will be rightly proud to have one of their own as Premier," Ms Archer said.

Tasmanian Liberal senator Wendy Askew said she was thrilled Tasmania will led by a Bass-based member.

Tasmanian Liberal senator Jonathon Duniam said he was positive Tasmania would continue to make positive gains under Mr Gutwein's leadership.

Tasmanian Liberal senator Claire Chandler said she was confident Mr Gutwein would steer the state on a positive bearing, with a focus on job creation, continued economic growth and improved services for all Tasmanians.