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 prop up the Liberals with parliamentary votes of confidence and supply.
Signed agreements between Premier Jeremy Rockliff and independent MPs Kristie Johnston and David O'Byrne were made public on Wednesday.
Tasmanian Independent David O'Byrne sitting in state parliament last year. (Rob Blakers/AAP PHOTOS)
"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 they 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 certain processes and 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 will consider government legislation on its merits and will have regular meetings with the premier and ministers.
The agreement is void if Mr Rockliff is not premier.
Ms Johnston has agreed to provide confidence and supply on "merit" and will continue to consider every issue at face value.
Her vote of confidence exists 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.
"In addition, 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."
The third independent MP in parliament, fisherman Craig Garland, recently said he had not been approached by Mr Rockliff with a formal deal.
The election was held ahead of schedule after the Liberals were unable to resolve a stand-off in minority with two crossbenchers who weren't returned to parliament.
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