Egypt international Hegazi has been ever-present for the Baggies in the Premier League this season, but has been unable to prevent their slide into the drop zone.
The defender scored on his debut to seal a 1-0 win over Bournemouth on the opening day of the season, but West Brom have not won since the fixture which followed – a 1-0 win at Burnley – leading to the departure of Tony Pulis as head coach.
Replacement Alan Pardew is yet to oversee a win but Hegazi believes an upturn is around the corner.
"I am very happy with the club and very happy to be part of this group of players," he told the Baggies' official website.
"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 sit in 19th place in the table following their 2-1 home defeat to Manchester United on Sunday.