Pernis signed a pre-contract agreement with United in July and the Clydesdale Bank Premier League side tried to secure his early release from the Slovakian's parent club.
Initially Zilina refused to free him from his deal, which was set to expire at the end of this month but have now relented and Pernis is now expected to make his debut on January 9 in the Active Nation Scottish Cup against Partick Thistle.
Boss Craig Levein told the Evening Telegraph: "He's got big boots to fill in Nicky's, but he trained with the lads and I was pleased with what I saw.
"I've got good contacts in Slovakia and they've been full of praise for him and feel he'll be challenging for the number one spot in their national team in the next couple of years."
Levein is delighted Pernis will have a month or so to bed in at Tannadice.
He said: "That's why we've got him here just now. I didn't think it was going to happen, but his last club agreed to cancel his contract.
"That will allow him and his family to settle in and, it's credit to the rest of the lads, I'm sure he'll settle in quickly with the team."