As many skeptics have asked this question, is Astrology really Vedic, because we say Astrology is a Vedanga. Where in Vedas there is mention about Astrology or Jyotisha ?
They accept Vedas but are not ready to accept Astrology/Jyotisha to be a part of the Vedas, hence they ask us to prove with reference to Vedas. Therefore this is a humble attempt to clarify this question.
At the outset this question “Is Astrology Vedic ?” itself is INVALID, this is just like asking “Is Algebra a part of Mathematics ?”, if yes then prove where in Mathematics it is said Algebra is a part of it.
The below chart gives the flow of Vedic Knowledge in-detail:
Muṇḍaka Upaniṣad (1.1.4-5):
dve vidye veditavya iti, ha sma yad brahma-vido vadanti
parā caivāparā ca tatrāparā ṛg-vedo yajur-vedaḥ sāma-vedo ’tharva-vedaḥ
śikṣā kalpo vyākaraṇaṁ niruktaṁ chando jyotiṣam iti
atha parā yayā tad akṣaram adhigamyate.
"There are two kinds of educational systems. One deals with transcendental knowledge [parā vidyā] and the other with material knowledge [aparā vidyā]. All the Vedas — the Ṛg Veda, Yajur Veda, Sāma Veda and Atharva Veda, along with their corollaries, known as śikṣā, kalpa, vyākaraṇa, nirukta, chanda and jyotiṣa — belong to the inferior system of material knowledge [aparā vidyā]. By parā vidyā one can understand the akṣara — Brahman or the Absolute Truth."
Sham no grihaashchandramasaah
Sham no mrithuh dhoomaketu
Sham no rudrasthigma tejasah
May we get welfare from the planets like the Moon, Mars, Mercury, Jupiter, Venus & Saturn. May we get welfare from the Su as well as from the Rahu, may we have welfare from Mrithyu ad Dhoomketu, may we receive welfare from Rudras with fierce rays.
Navo navo bhavati jayamaanohnam
Bhagam devebhyo vidadhatyaayan
Prachandrama sthirathe dheergam ayuh
The Moon becomes new and new (with the addition of brightness each day) and thus acting as ahnam ketu or indicator of thithis (Lunar dates). Ushasametiagram goes ahead of the sun. in the Aayana paksha (bright nights) it devebhyo bhagam vidadhaati imparts its influence to the nakshatras (asterisms) verily the Moon gives us long life.
Atharva Veda 19 kanda 7.2
Suhavmagne krithika rohini chasthu
Bhadram mrigashiraa shamardho
Punarvasu sunathaa charu pushyo
Bhanur ashlesha ayanam magha me
Atharva Veda 19 kanda 7.3
Chitraashivaa swati sukho me
Asthu raadhevishaake suhavanuradha
Srimad Bhagavatam 1.12.29
iti räjïa upädiçya
pratijagmuù svakän gåhän
Thus those who were expert in astrological knowledge and in performance of the birth ceremony instructed King Yudhiñöhira about the future history of his child. Then, being sumptuously remunerated, they all returned to their respective homes.
jyotiñäm ayanaà säkñäd
yat taj jïänam aténdriyam
praëétaà bhavatä yena
pumän veda parävaram
O great saintly person, you have compiled the astrological knowledge by which one can understand past and present unseen things. By the strength of this knowledge, any human being can understand what he has done in his past life and how it affects his present life. This is known to you.
The Vedic understanding is that every aspect of life is sacred. That is why each significant stage.