The Liberals, who have been in power since 2014, won 14 of 35 lower-house seats at the March 23 election - four short of a majority.
Three first-term Jacqui Lambie Network MPs in early April signed an agreement to provide the Liberals with parliamentary votes of confidence and supply.
Premier Jeremy Rockliff had been in talks with independent MPs David O'Byrne, Kristie Johnston and Craig Garland to shore up the additional vote required.
Signed agreements between Mr Rockliff and Ms Johnston and Mr O'Byrne for confidence and supply were made public on Wednesday.
"The agreement provides confidence and supply in the forthcoming parliament," Mr Rockliff said.
"I thank both members for their goodwill and constructive input which have been in the interests of ensuring the stability and certainty Tasmanians desire and deserve."
Mr O'Byrne, a one-time Labor leader, said he had an obligation to work with Mr Rockliff after his former party conceded it could not govern with just 10 seats.
In the signed agreement, Mr O'Byrne said he was prepared to offer a commitment of confidence and supply, subject to conditions.
He will back the Liberals in the face of parliamentary no-confidence motions except when corruption, gross incompetence, serious misbehaviour or failures of policy and governance are involved.
Mr O'Byrne said he would vote on government legislation on its merits and would have regular meetings with the premier and ministers.
The agreement is void if Mr Rockliff is not premier.
Independent David O'Byrne said he would vote on government legislation on its merits. (Rob Blakers/AAP PHOTOS)
"I have always been a staunch critic of successive Liberal governments in Tasmania, governments that have failed to improve government services and failed to improve the lives of Tasmanians," Mr O'Byrne said.
"However, dragging Tasmanians back to the polls prematurely is not the solution that our state needs right now."
Tasmania went to an early election after the Liberals were unable to resolve a stand-off in minority with two crossbenchers who were not returned to parliament.
Ms Johnston will provide confidence and supply on "merit" and will continue to consider every issue on face value.
She is chasing boosted staffing and office improvements.
Her vote of confidence is maintained if the government is "transparent and accountable", there is a high degree of integrity in parliament and decisions are made in the best interests of Tasmanians.
"My consistent stand since the election has been that the party commissioned to form government should be given a chance to govern," Ms Johnston said.
"I've also consistently said that I am prepared to provide confidence and supply on a merit basis so that the government can get on with its job."
Labor leader Dean Winter criticised Ms Johnston for not explicitly getting outcomes for voters in the "deal".
"It will be interesting to see how long (support) lasts if the Rockliff Liberal government fails to perform or uphold its commitments," he said.
The Jacqui Lambie Network MPs - Andrew Jenner, Miriam Beswick and Rebekah Pentland - can also vote against the government but are subject to more conditions.
Parliament returns on May 14.
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