Premier Jeremy Rockliff said with the 35 members of the state's assembly elected, 13 of them new faces, he would advise Governor Barbara Baker that he be recommissioned to form a new government.
The incumbent Liberals will have to cobble together a minority arrangement with cross-bench support after falling short of the 18 seats required for majority at the March 23 poll.
The party has been in power since 2014.
One seat, in the northwest electorate of Braddon, remained undecided on Friday as the distribution of preferences continued.
Mr Garland, an independent, campaigned in Braddon against industrial offshore aquaculture.
ABC election analyst Antony Green said on Saturday afternoon Mr Garland was 943 votes ahead of the seat's fourth Liberal candidate, Giovanna Simpson, with not enough ballots remaining to change the result.
"I am confident we now have a parliament comprised of members who are committed to providing the stability and certainty that Tasmania needs and who will put the best interests of Tasmanians first," Mr Rockliff said in a statement."The new government will be steadfast in its commitment to delivering every element of the Liberals' 2030 Strong Plan for Tasmania's Future."He also promised to treat the outcome of the election with "respect and maturity" but again ruled out doing deals with the Greens or trading ministries.
Mr Rockliff said his constructive and positive discussions with Jacqui Lambie Network members and independents continued.
Mr Garland has previously described himself as an "anti-politician" and accused parties of hijacking democracy for their survival.
He has run at several state elections and picked up more than five per cent of the first-preference vote.
A third of Tasmanians snubbed the two major parties at the election, with the Liberals receiving 37 per cent of the primary vote and Labor 29.
Labor, which picked up just 10 seats, conceded it was unable to form government the day after the election.
The crossbench will also include independents David O'Byrne and Kristie Johnston.
Senator Jacqui Lambie, who hails from Tasmania's northwest, has indicated her party is prepared to provide stability to the Liberals.
Each of Tasmania's five electorates is represented by seven MPs under the Hare-Clark proportional voting system.
