As far as I understand, the sentence does not give information about the “winner” (you have translated it by “lauréat” which is correct) but only that the scholarship has been awarded. So the beginning would be “Bourse XYZ attribuée”

“après sélection de 1000 candidats” is not correct as you said because I think the candidates have already applied to intend the competition.

“niveau mondial” sounds a bit odd to me, it does not seem to be the correct translation for “around the world”. You may rather think about an international competition.

I can suggest

Bourse XYZ attribuée à l’issue d’un concours international impliquant 1000 candidats.

“à l’issue de” means “as a result” and “impliquant” would be “involving”

"Sélection de 1 000 candidats" would indeed mean that 1000 candidates were selected, but "sélection parmi 1 000 candidats" would mean you were selected amongst the 1 000. Apart from that, there is no problem with what you proposed, but it could be improved a bit.

The translation of "competing" depends on the exact nature of the competition. "Concours" means "contest", so you had to do something specifically for the contest and were evaluated on… some criteria. For other forms or selection, based on your academic file or anything, it wouldn’t fit. Without more context and details, the "one size fits all" answer could simply be "parmi", which just means "amongst".

"Lauréat" is a good fit but a bit pedantic; not enough to change it, but you might want to lighten the rest of the sentence a bit.
So a final version could be, depending on exactly how you got that scholarship :

Lauréat de la bourse XYZ parmi 1 000 candidats au niveau mondial.

Lauréat de la bourse XYZ à l’issue d’un concours impliquant 1 000 candidats du monde entier.

Lauréat de la bourse XYZ après sélection sur dossier parmi 1 000 candidats dans le monde.

Or any mix of these. As @Coriolis pointed out, "concours international" would fit too.