If you have this question what should be practiced first Yoga Asana, Pranayama, or meditation then you are not alone. I would quote a very famous Hatha Yoga book here to answer this question. Hatha Yoga Pradipika commentary by Swami Muktibodhananada (Yoga Publications Trust, Munger, Bihar, India) explains:
After asanas, pranayama should be practiced to purify the nadis. For this purpose nadi shodhana (nadi purification) pranayama is best. Then mudras should be performed to channelize the energy and create specific attitudes of mind, and bandhas to force the energy upward. In hatha yoga the sequence is – Asanas first, then Pranayama, Mudras and Bandhas. Lastly one should sit quietly in a meditative pose.

Personally, I start my practice with Sukshma Vyayama or light exercises to loosen up followed by Asasanas, Pranayama, and then Meditation if I have full hour to practice. The asanas help remove physical blockages in the body and after performing Asanas the energy flows freely and you are able to sit comfortably to perform Pranayama. After Pranayama, it is easy to sit in a meditative state.

In the systematic science of Hatha Yoga, you must firstly prepare the physical body because it is the grossest manifestation of prana. Activate the prana through asana, then practice pranayama to purify the energy channels and to process and balance the prana.
In Hatha Yoga they say if you can control (regulate) your body and breath, you can control your mind to a greater extent.
Traditionally the right sequence or order is Asana, Pranayama, and Meditation at the end.
Reference:
Hatha Yoga Pradipika commentary by Swami Muktibodhananada.
Originally हठयोगप्रदीपिका Hatha Yoga Pradipika, the most influential texts on traditional Hatha Yoga was written in Sanskrit by Swami Swatamarama in 14th Century. He was a Nath yogi, associated with the Nath tradition, which traces its roots to Matsyendranath and Gorakhnath.
About The Author
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Neeraj Kumar is a Yoga Enthusiast and a Real Estate Business owner in Metro Vancouver. He is an active member of the Vancouver Indian Community. Visit www.linkedin.com/in/kumar-neeraj to connect with Neeraj on LinkedIn.