The deal includes an assessment of financial modelling behind a divisive stadium and an earlier youth detention centre shutdown.
The Liberals, who have been in power since 2014, have been courting crossbench support after winning 14 of 35 lower-house seats at the March 23 poll - four short of a majority.
Jacqui Lambie Network first-term MPs Miriam Beswick, Andrew Jenner and Rebekah Pentland on Wednesday inked a deal for "stability" with Premier Jeremy Rockliff.
The Liberals remain in talks with three independents to sure-up the one additional vote of support required to form government.
The network MPs have agreed to support the Liberals on confidence and censure votes, appropriation and revenue bills and on parliamentary motions that bind the government.
They can bring forward legislation and motions and vote against the Liberals on legislation and legislative amendments if they abide by a "stability protocol".
Under the protocol, they must give 24 hours notice of their vote and first undertake "good faith" negotiations to try to reconcile their position.
"All parties have entered into this agreement with goodwill and trust," Mr Rockliff said in a statement.
"I am confident that this agreement will provide the long-term certainty and stability the Tasmanian people expect."
The signed agreement, which has been made public, will be reviewed after 12 months.
It contains a condition for an independent review of Tasmania's budget within six months, including financial modelling behind Hobart's Macquarie Point project and stadium.
The $715 million waterfront stadium, which requires parliamentary approval, is a condition of Tasmania's entry into the AFL in 2028.
Senator Jacqui Lambie has been a vocal critic of the stadium spend amid a health, housing and cost-of-living crisis.
There is also a condition for the closure of the troubled Ashley Youth Detention Centre within the 12 months of the agreement.
The Liberals, which in 2021 pledged to shut the centre by the end of 2024, have a revised mid-2026 closure.
The final report of an inquiry into child sexual abuse in government institutions, released in September, called for the centre to shut as soon as possible amid ongoing risks.
The network MPs will also get a confidential briefing before the budget and can put forward "budget bids" for consideration.
There will also be a review of the state Integrity Commission with an eye to giving the body greater capability, plus a review of right-to-information and political donation laws.
In a joint statement, the network MPs said they were "fully committed" to ensuring greater integrity in politics.
Greens leader Rosalie Woodruff described the agreement as lacking substance.
"(The network members) have not received any concrete or specific commitment to reform," she said.
"A nod, a wink, or a review is not the same as getting an (Independent Commission Against Corruption) or any other real, meaningful change."
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