Hinkley boarded a flight from Melbourne to Hobart on Sunday to meet with Devils officials and deliver his final presentation to the board.
Tasmania's social media accounts teased the announcement on Sunday evening.
Former Collingwood coach Nathan Buckley and ex-Sydney boss John Longmire were the two other main contenders for the Devils coaching job.
But Hinkley has been picked by the Devils' hierarchy, and AAP understands the decision will become official at a press conference in Hobart on Monday.
Buckley is set to remain an assistant at Geelong next year after being overlooked for the Devils role, while premiership coach Longmire will be heavily linked with any senior job arising over the next 12 months.
Longmire met with the Devils a fortnight ago in what he described as a fact-finding mission.
He remains at Sydney as the club's director of club performance, exiting the senior coaching role after the Swans' 2024 grand final humiliation against the Brisbane Lions.
Hinkley coached Port from 2013 to 2025 but famously failed to reach a grand final in those 13 seasons, losing three preliminary finals along the way.
It meant Hinkley exited Port with the unwanted mark of having coached the most VFL/AFL games without reaching a grand final.
Nevertheless, the 59-year-old walked away with an excellent winning record of 58.6 per cent, having guided Port to 174 victories from his 297 games in charge.
A recent report suggested axed Essendon coach Brad Scott could take up a football boss role at the Devils.
But Devils football director Alastair Lynch, an ex-teammate of Scott during their Lions days, has since dismissed that prospect.
The Devils will enter the AFL in 2028 and have been granted a host of generous draft concessions to ensure they will be competitive from the get-go.
Among those concessions, Tasmania will have picks 1, 3, 5, 7, 9, 11 and 13 in the 2027 national draft, but they must trade picks 5, 7, 11 and 13 to other clubs for either players or other draft picks.
They can also sign up to 18 uncontracted players from rival sides across 2027-28, snaring a maximum of one player per club.
Tasmania are currently in eighth spot in the VFL, having posted eight wins, six losses and a draw in a promising campaign to date.
The Devils aren't the only club closing in on a new coach.
Essendon are narrowing down their search for Scott's replacement, with the role set to come down to former club great James Hird and current interim Dean Solomon.
Carlton are also on the lookout for a new coach after parting ways with Michael Voss earlier this year.
Interim Blues coach Josh Fraser initially said he didn't want the role full-time, but his name is well and truly in the mix since he has guided Carlton to seven wins from his nine games in charge to date.
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