The standard Europe 101 argument (and I just gave a lecture on it last week) is:

• by building a state bureaucracy of non-noble, paid staff (instead of offices that would be handed to aristocrats)

• by having loyal administrators, Intendants, travel to distant areas and keep an eye on things;

• and by building Versailles... a huge symbol of status and power... and then inviting the most powerful nobles in the realm to come live there. (and distribute "favors," such as the opportunity to dress him in the morning, which translated into access.)

But a cooler, much more sophisticated argument--too complex for my 101 class, unfortunately-- is in William Beik's book on Absolutism, which basically shows how it's just as much a bottom up process... namely, all the aforementioned things (bureaucratic state-building, Versailles) were going on, of course,

... but the key factor became when the great nobles (Anjou, Berry, etc) started to perceive this growing "state" of Louis XIV's monarchy as an opportunity--as an avenue to advance their own interests.

So, imagine the Duc de Berry in competition with the Duc d'Anjou; instead of a futile (and often deadlocked) direct struggle of rallying their own supporters, resources, etc., the could now turn to the growing state--and use it to press their own claims to their own advantage.

Short version: once the great nobles saw that they could use Louis XIV for their own interests, they increasingly made Louis the de-facto "center" of power... and thereafter could be increasingly coopted by him...