Hegazi initially joined the club in July on what was intended to be a season-long loan, but the Baggies held an option to sign the defender permanently and have now chose to do so.
The towering 26-year-old, who will be going to the World Cup with his country in the summer, has started all 18 of West Brom's Premier League games so far this season and has signed a long-term contact with at The Hawthorns until June 2022.
"I am very happy with the club and very happy to be part of this group of players," Hegazi told WBA.co.uk.
"I know the results are not what we would want at the moment. But there is great spirit here and I am sure that we will turn the results in our favour before long."
West Brom boss Alan Pardew added, "This is great news for the club - Ahmed has been absolutely terrific for me since I arrived and I am sure there is even more to come from him in the future.
"He is one of the players we can build around on the road ahead. He has a big role to play and it is good for the player and the club to remove any doubts and make the transfer permanent.
"I'm sure it is something the supporters will also welcome."