It is a common error to treat meditation as an Asian import into a West that had nothing of the kind. The Christian, Jewish and Muslim contemplative traditions are large, old and continuous.
Christian contemplation runs from the Egyptian desert monks of the fourth century through the Byzantine hesychasts, the Rhineland mystics, the Carthusians and the Spanish Carmelites. The Cloud of Unknowing, written anonymously in fourteenth-century England, instructs the reader to fix on a single short word and let everything else fall away beneath a deliberate forgetting, structurally very close to mantra practice its author had certainly never heard of. The Spiritual Exercises of Ignatius of Loyola go the opposite way, into detailed and deliberate imaginative construction of scenes, closer to Tibetan visualisation than to anything in the apophatic line.
Jewish contemplative practice includes the intentions attached to specific words of the liturgy, the letter permutations taught by Abraham Abulafia in the thirteenth century, and the Hasidic practice of secluded spoken meditation.
Islamic dhikr is a sustained repetition discipline with a fully developed literature on its stages, its physical effects and its characteristic dangers.
What is genuinely new is the twentieth-century transmission of Asian techniques to Europe and North America with the religious framing removed, and then the return of that stripped form into the traditions that produced it, so that Buddhist teachers now sometimes learn a secularised version of their own practice. That is a real and interesting historical development. It is not the arrival of contemplative practice in the West, and describing it that way erases a great deal that is still being practised.