Your translation is grammatically correct so “L’article dit que …” works in this case, it’s understandable and good if you want to translate literaly (but still correctly).

However, you might want to use a better verb like “expliquer” : “L’article explique que courir est bon pour votre santé”.
“Expliquer” means “explain” but it is more idiomatic here.

[EDIT]
About the “votre santé”, it is true that “la santé” would also be better. The translation is still okay without this modification.

[EDIT2]
IMPORTANT Using “dit” is neutral whereas “expliquer” can be used to say that the article explains in details. The best formula here would be D’après, used like this :

D’après l’article, courir est bon pour la santé

This sentence now says that the article as a whole states that running is good for your health.

One could use

Selon cet article

and close to @matthieusb proposal, I think that

D’après cet article

could fit as well.