ّThe practice is based on several reports, amongst them:
Ibn Salam asked the Prophet (S) a number of questions, one of which was, "O Muhammad (S), teach me how to begin and end the recitation of the Qur'an"
The Prophet replied, "Begin with بسم الله الرحمن الرحیم and conclude with صدق الله العلی العظیم"
Majlisi, Bihar, v57, p.243