The 24-year-old has joined Martin O'Neill’s side on an initial four-year deal, with the club having an option for a fifth.
Sky Sports have reported that the clubs have agreed an initial fee of £6 million, which could rise to £9m through various performance-related add-ons.
It’s understood a significant portion of these bonus payments will be triggered if Celtic reach the league phase of the Champions League later this month.
Speaking to the club’s website, the Egypt international expressed his excitement in joining the club.
"At 24, I think it’s a good moment for me to move away from Spain. I’ve been there for six years," Hassan told CelticPlayer.
"With Celtic’s history, all the great players, the fans and the atmosphere, I think this is the perfect moment for me.
“I know I’m joining a big club, the biggest club in Scotland, and I’m really looking forward to taking the next step."