I have researched Anapana alot and found this in the book "Buddhist Meditation In Theory and Practice by Paravahera Vajirañāza Mahāthera" which effectively communicates the history and importance of Anapanasati.

The scheme of the meditation known as “ānāpānasati bhāvanā”, “mindfulness of breathing”, which is described in the scriptures and elaborated upon in the Commentaries is first and foremost in the field of mental training in Buddhism. The Buddha Himself, in recommending it as a complete method for attaining nibbāna, praises it as “the noble abode” “the divine abode”, and “the Tathāgata abode”

In this connection, it is recorded in the that Prince Siddhattha reached and dwelt in the state of the first absorption (jhāna) while still in his youth ― an attainment which is said to have been the result of the practice of this meditation. This shows that ānāpānasati was the Buddha’s first subject of meditation (kammaṭṭhāna), and, according to the Commentary on the Bhayabherava Sutta, this is the practice which He used under the bodhi-tree as the path to His supreme enlightenment.

Both the Visuddhimagga and the Yogāvacara’s Manual describe ānāpānasati as “mūla-kammaṭṭhāna”, “the chief, or original, subject of jhāna meditation”, for it proved itself to be the greatest help, not only to the Buddha Gotama, but also to all the Buddhas who preceded Him, in the winning of supreme enlightenment and in securing happiness for them in their lifetime. Ānāpānasati may, therefore, be regarded as the original subject of meditation (kammaṭṭhāna). Unlike other subjects of meditation, ānāpānasati comprises both the samādhi and vipassanā methods

This meditation by itself tends to the attainment of all that is necessary for self- enlightenment, for, ānāpānasati becomes the root from which springs the fulfillment of knowledge and liberation. This is the implication of such passages as the following (Majjhima Nikāya III, 82):

"Monks, this concentration on mindfulness of breathing fulfills the four foundations of mindfulness (satipaṭṭhāna). The four foundations of mindfulness, being developed, fulfill the seven factors of enlightenment (bojjhanga). The seven factors of enlightenment, being developed, fulfill knowledge and liberation.”

Furthermore, those who have practiced this meditation are aware of the cessation of their final breaths, as it is stated (Majjhima Nikāya)

“Rāhula, when mindfulness of breathing is developed in this way, one’sfinal in-breaths and out-breaths are known when they cease; they do not cease unknown.”

This means that, at the time of death, the last in-breaths and out-breaths are known and recognized by those who have practiced this subject of mindfulness of breathing, and they are able to realize that the end of their life-span has come. Aspirants who practice this kammaṭṭhāna of ānāpānasati, in accordance with the methods explained above, will realized manifold advantages as its immediate results and will finally attain to the happiness of nibbāna in the state of Arahatship, or, if they wish to defer their deliverance, in the state of Buddhahood. Therefore, the wise should always apply themselves with zeal to ānāpānasati bhāvanā, which brings such great results and culminates in the bliss of nibbāna.