Speaking to the club's official website Pulis said: "We're pleased he's here, he's a good addition".
"We're delighted to add Ahmed to the squad".
Hegazi has flown out to Hong Kong to link up with the West Brom squad ahead of their Premier League Asia Trophy game with Premier League rivals Leicester on Wednesday, although he will need global clearance to play in the tournament.
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"We will use the deal's fee to bolster the team with new signings to make Ahly stronger in the coming period", he added. "He caught our eye at the African championships and we've been tracking him ever since". It's really, really good for us'.
As revealed by the Express & Star last week, Albion decided to make a move for Hegazi after baulking at the £8m loan fee Chelsea demanded for Kurt Zouma.
Hegazy will be the fourth Egyptian player in the English Premier League next season alongside Arsenal's midfielder Mohamed Elneny, Stoke City's winger Ramadan Sobhy and Liverpool's newly signed winger Mohamed Salah.
He spent half a year in Serie B with Perugia before joining Al Ahly on a five year deal in 2015.