Former Arsenal youngster Stack will put pen to paper on a two-year contract at Easter Road and will battle Yves Ma-Kalambay for the number one jersey.
The 27-year-old fell out of favour with Pilgrims boss Paul Sturrock shortly after his arrival on a free from Reading and was told he had no future there.
Stack is now poised to join the Hibs squad in Belfast for their pre-season friendlies against Glentoran and Shamrock Rovers.
He told the Daily Record: "Everything has been agreed with the contract and it's just a case of getting it signed.
"I've reached a settlement with Plymouth to release me from my contract and allow me to walk away from the club.
"I'm delighted Hibs have shown a lot of interest in taking me up to Scotland, especially the gaffer who I had a conversation with last season when he was at Falkirk.
"I had offers from three or four League One clubs and a Championship side but I chose Hibs and I'm looking forward to playing football again because I didn't really settle last season.
"Having started the season with Plymouth, I had some differences with the manager and he decided to leave me out.
"He then made it clear I didn't have a future at the club, even though he said he thinks I'm a good 'keeper."
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