Premier Jeremy Rockliff met with Governor Barbara Baker on Wednesday at Government House to formally ask for his minority government to remain.
Ms Baker accepted the request after Mr Rockliff told her he expected to gain the confidence of the lower house, the governor revealed in a statement.
"In a hung parliament, where no one clearly holds the confidence of the majority of the House of Assembly, the incumbent has the right to remain in office in order to test the numbers in the House of Assembly and for Parliament to have the final say in who should be Premier," Ms Baker said.
"I consider the convention of incumbency applies in the current circumstances.
"I shall reappoint the Premier.
"It is better for confidence to be determined inside and not outside the Parliament."
Mr Rockliff and his cabinet are set to be sworn in next week, before state parliament returns in a fortnight on August 19.
The governor said the detailed reasons for her decision would be published on her website later on Wednesday.
On Tuesday, Mr Rockliff said he had not secured supply and confidence agreements with key crossbenchers but thought it was "not necessary" in this instance.
Labor leader Dean Winter was still vying for his party to form government, revealing he had stepped up negotiations with crossbenchers, independents in particular, in recent days but ruled out a deal with the Greens.
The final makeup of Tasmania's parliament is 14 Liberals, 10 Labor, five Greens, one Shooters, Fishers and Farmers MP and five independents.
The July 19 election was triggered after Mr Rockliff lost a no-confidence motion, prompting the state's second election in 16 months.
A key sticking point in forming government is the major parties' backing of a new $1 billion stadium in Hobart, which the Greens and some independents oppose.
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