The 26-year-old has been on loan from Al Ahly, joining Albion in July, and the option has been taken to prolong his stay at The Hawthorns.
An undisclosed fee has been agreed between the two clubs and Hegazi has signed a contract until the summer of 2022.
Hegazi was brought to the club by former boss Tony Pulis but new manager Alan Pardew has welcomed the decision to keep the player.
He told the club's official website: "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."
West Brom are without a Premier League win since August and sit in the relegation zone after Sunday's 2-1 home defeat to Manchester United, but Hegazi had no hesitation committing his future to the club and is confident things will improve soon.
"I am very happy with the club and very happy to be part of this group of players," he said.
"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."
Hegazi marked his West Brom debut by scoring the only goal in a home victory over Bournemouth on the opening day of the season and has gone on to make 19 appearances for the club.
Source : PA