The Frenchman moved to The Hawthorns on loan from Nancy during the transfer window and he will stay with West Brom until the end of the season.
He has already made an impact, scoring two fine goals in the 3-2 defeat by Newcastle earlier this month.
Mowbray asked Fortune to lead the attack against Newcastle and the Baggies manager feels he will continue to improve as he adjusts to English football.
"I felt in his first couple of games he played as part of a strike partnership but I wanted him to take on the mantle of leading the line," said Mowbray.
"I thought he did that exceptionally well. That's how I'd seen him play in France, almost like a target man. He's got the technical ability to help bring in other players.
"He should be confident in his own ability to get hold of the ball for the team. I think he showed that against Newcastle.
"He did well and took his goals well. He got hold of the ball, brought people in and looked a threat."
ConfidenceMowbray thinks Fortune has all the attributes needed to succeed in the Premier League and could help West Brom avoid the drop.
He said: "All strikers need to score goals to get that confidence and belief that they belong and are part of something.
"Coming from abroad, it's sometimes hard to instil your personality on the team. But as he grows he could become the catalyst for the team.
"You see sometimes with the best strikers they have an arrogance or cockiness about them where they want the ball and say 'I'll score'.
"There are signs he is growing into that and hopefully the Newcastle game will help that a lot.
"He's shown me from day one he can score goals. He's got two good feet, shoots with either of them, spins both ways and strikes the ball well."