The Parkhead club have been long-term admirers of the Danish forward and reignited their interest in the player last week.
Now, Celtic have reached an agreement to sign the 25-year-old for an £11m-plus transfer fee. The deal is set to eclipse the previous record amount paid for Arne Engels.
Hogh is expected to undergo a medical ahead of the proposed move to Celtic in the coming days.
The player is thought to be ready to pen a long-term contract with the Scottish Premiership champions.
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The news comes shortly after Daizen Maeda completed his transfer exit from Celtic to sign for Premier League side Ipswich Town.
After his transfer, worth up to £10m, was announced, the Japan forward posted an emotional farewell message.
He wrote: “To the Celtic family,
“The last four and a half years at Celtic have been the most special chapter of my career and my life.
“It has been an incredible honour to wear this badge, to play for this amazing club, and to share so many unforgettable moments with my teammates, the staff, and the best supporters in the world.
“Thank you for standing by me through every high and low. Your incredible support gave me strength every single day, and I will always be grateful.”
