Jeremy Rockliff returned to Government House on Wednesday evening to meet with Governor Barbara Baker, six days after he lost the confidence of the parliament.
In a statement after the meeting, Ms Baker confirmed she would dissolve parliament and issue the writ for an election to be held on July 19.
It will be the fourth state election in seven years after early polls were also held in 2021 and 2024.
"Notwithstanding the recent 2024 election, the public interest in avoiding the cost of another election and the prevailing public mood against holding an election, I have granted Premier Rockliff a dissolution," Ms Baker said in the statement.
"I make this grant because I am satisfied that there is no real possibility that an alternative government can be formed."
Mr Rockliff has resisted pressure to resign and insisted the backing of his partyroom remains solid, despite reports former senator Eric Abetz and ex-deputy premier Michael Ferguson were willing to be leader.
"I have a commitment from my team to support me as leader and I am not going anywhere," he said earlier on Wednesday.
Mr Rockliff denied he was "driven by ego" in not standing aside from leading the minority government.
Liberal MP Jacquie Petrusma didn't directly answer when asked if the party was doing numbers to roll Mr Rockliff.
"The premier is a fantastic leader and he has 100 per cent support of the PLP (parliamentary Liberal Party)," she said.
Ms Baker also met Labor leader Dean Winter on Wednesday afternoon.
Labor, which has just 10 of 35 lower-house seats, had said it would not look to form a minority government with the Greens.
"In that meeting (with the governor) I reiterated my position that Labor will not be doing a deal with the Greens," Mr Winter said.
Labor, whose no-confidence motion against Mr Rockliff was backed by the Greens and three crossbench independents, had called on the premier to step down.
"We've gotten to this point because of Jeremy Rockliff and his refusal to resign," Labor MP Shane Broad said.
"I come from a farm and no matter how much you love that old sheep dog, if you can't round up sheep anymore it's time to get a new one."
Mr Rockliff claimed the no-confidence motion was a deceptive power grab, while Labor says it was because of the Liberals' poor budget and project mismanagement.
The premier took a crack at Mr Winter for failing to "front up" and hold a press conference on Wednesday.
The Liberals had already appeared to be in fully fledged campaign mode, visiting a hospital to announce a four-year elective surgery plan.
They were returned to power in March 2024, winning 14 seats and cobbling together enough support from the crossbench to govern.
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