Chairman Fawaz Al Hasawi has vowed to strengthen Nottingham Forest year on year, with loan arrivals possible.
A number of English clubs are tracking Helsingborgs hot-shot David Accam, Sky Sports understands.
The 31-year-old has signed a three-year deal at the KC Stadium as the Tigers continue to prepare for their return to the Premier League.
McGregor told Hull's website: "I'm really excited to be here and I'm happy that everything is done now.
"I can't wait to get started here. This is a great chance for me to play in the Premier League and I'm looking forward to the season ahead."