Firmus Technologies' 288MW factory at Bell Bay on the island's north was on Tuesday given planning approval by the local council.
It comes as the federal government is soon expected to finalise rules on how data centres use energy, while South Australia recently announced it would hold a royal commission into their operation.
Firmus is also building a 104MW data centre in Launceston in Tasmania's north and wants to build a 52MW centre at Wesley Vale in the northwest.
Community groups have raised concerns about noise, energy and water use, as well as a claimed lack of consultation, with 6000 signing a petition against the Bell Bay proposal.
More than 9000 people have signed a petition to parliament calling for a moratorium on all uncompleted AI and data facilities until greater oversights are established.
Tasmanian Premier Jeremy Rockliff said he welcomed AI investment, noting it was important there were guardrails on the technology.
"(But) we don't want to see those guardrails become too restrictive. We want to ensure that Tasmania is open for business," he told reporters.
State Greens MP Tabatha Badger said future generations may bear the burden if Tasmania isn't careful with resource allocation.
Approval for the centre means Firmus will become the state's biggest power user.
"The push to ram through these resource intensive facilities before any binding guardrails are in place is not only inappropriate but incredibly risky," Ms Badger said.
"The decision was made just 24 hours before a federal cabinet meeting discussing nationwide obligations around energy and water consumption of AI and data centres.
"(It) is an added insult to the community."
The Bell Bay centre will create 380 jobs during construction, 115 ongoing jobs and use 8.7 million litres of water per year, less than what three typical restaurants use annually, Firmus says.
It will draw power from Tasmania's grid which is largely green energy.
Firmus has previously said at full capacity the noise heard by the nearest resident one-to-two kilometres away would be "less than what you hear when you walk into a library".
The council has placed several conditions on the project, including making Firmus undertake a noise survey within 60 days of starting operations.
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