I want to know about the history of Bhagwat Maha Purana. Was it written by someone or is it God's own words?
Puranas are smritis written by men. Every Purana is a narration by a learned person to a seeker - may be a Maharishi, a common human being or a learned sage. The seeker in Srimad Bhagavatam is Kulapati Shaunaka at his Naimisharanya Hermitage and the question is directed at Maharishi Ugrashrava, the son of the Suta Sage Lomaharshana (Romaharshana). Maharishi Ugrashrava is commonly referred to as Suta, even though he is not one. Maharishi Shaunaka often addresses him as Sutanandana or son of Suta.
The Purana was composed by Maharishi Krishna Dwaipayana - the twenty eighth Vyasya (current) of the Vaivatawa Manvantara. He narrated it to his son Mahrishi Suka and his other disciples including Maharishi Maitrayee, Ugrashava (Suta) and others. This tale is the tale narrated by Sukacharya to Maharaja Parikshit after he was cursed to die within a week by Rishi Shringi. And hence there are portions where Maharaja Parikshit asks questions and they are answered. We are given the rendition of the same by Maharishi Suta at the Naimisharanya hermitage of Maharishi Shaunaka.
I really do not know of any Purana or Smriti wherein the story of composition of Srimad Bhagavatam is mentioned,but then my learning is limited and is someone enlightens me with the source, I shall be grateful.
The source The first paragraph itself makes it clear the source is Simad Bhagavatam itself. In verses 4 and 5 of Chapter 1 of Canto I it is said :
नैमिषेsनिमिषक्षेत्रे ऋषयः शौनकादयः | सत्रं स्वर्गाय लोकाय सहस्त्रसममासत ||
त एकदा तु मुनयः प्रातर्हुतहुताग्नयः | सत्कृतं सूतमासीनं पप्रच्छुरिमादरात् ||
At Naimisharanya Kshetra Maharishi Shaunaka and others were performing a fire sacrifice lasting 1000 years. After morning rituals, Maharishi Suta was offered an honoured seat and the assembled sages asked him to elucidate.......
In Chapter 2 of Canto I verse 1 reads:
व्यास उवाच : इति सम्प्रश्नसंहृष्टो विप्राणां रौमहर्षणिः | प्रतिपूज्य वचस्तेषां प्रवक्तुमुपचक्रमे ||
Vyaasa says "Hearing these questions from the learned rishis like Shaunaka, the son of Romaharshana Ugrashrava was greatly pleased. Thanking the learned rishis for their beneficial question, he started narrating as follows....
That this Purana was composed by Sri Veda Vyasa himself becomes apparent as one proceeds along Canto I first few chapters which I don't intend to reproduce here in full.