The Gunners head into their final Premier League game of the season knowing that three points at the Hawthorns will secure third spot, taking one step towards persuading Robin van Persie to stay at the club.
The Frenchman is hoping that his players can triumph, after a tough season in which they have shown "exceptional strength".
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"They have come through some difficult times, always recovered and always battled. Therefore I will be extremely delighted when we do it."
Tottenham Hotspur and Newcastle can take advantage if Arsenal slip up against the Baggies on Sunday, as they are only one point and two points, respectively, behind the Gunners.
Furthermore, fourth place may not be good enough to get into next season's elite European competition, depending on whether Chelsea manage to defeat Bayern Munich in this year's final.
Wenger therefore insisted his side must spoil Roy Hodgson's last game in charge of the midlands club by claiming victory, something he is confident will happen.
He added: "There is even more uncertainty because fourth place is not this time necessarily in the Champions League.
"Let's make sure we finish third and win our game - that is the only answer we can give.
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Wenger is without Bacary Sagna for the match, after the French full-back broke his leg in the 3-3 draw with Norwich, but Theo Walcott may return and Wojciech Szczesny is likely to shake off a back problem to continue in goal.
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