The Mirror says Baggies chiefs completed a transfer for the Egyptian international to join Saudi Arabian side Al-Ittihad just 24 hours before their Premier League clash with Brighton.
The 17th-placed Baggies travel to the AMEX Stadium on Monday night looking to pick up their first win of the season.
But Bilic's task was made all the more difficult when he learned that Hegazi - who started in last week's goalless draw with Burnley and had been expected to remain in the team - was departing.
Albion were offered a deal the board believed they couldn't refuse, banking £4million and saving another £3.5m-a-year in wages, with Hegazi's deal up in 2022.
But the situation has left Bilic far from happy.
After masterminding West Brom's return to the top-flight at the first time of asking, the popular Croatian was determined to bring in quality players to boost their survival chances.