The 73-year-old drummer - who founded the group in the 1960s - has agreed to the sale, which covers classic albums including 'Tango In The Night', 'Rumours' and 'Tusk'.
He said in a statement, "This is a wonderfully inspiring marriage between creative partners that understand all aspects of the business."
The agreement means Mick has traded his future earnings from the sale of the iconic group's music for an upfront payment, although BMG did not disclose the sum.
They noted the collection of albums covers 300 songs, or "18 hours of drumming".
BMG's Justus Haerder added: "This acquisition highlights the value of timeless recordings in a streaming market which is increasingly benefitting established rather than newer artists.
"Catalogues such as Fleetwood Mac's, which connect with every generation, are benefiting disproportionately from that growth."
The move comes after Mick's former bandmate Lindsey Buckingham's entire music catalogue was acquired by Hipgnosis Songs Fund.
Previously, the investment company - which is run by Merck Mercuriadis - had a 25 per cent share of the musician’s catalogue, but the firm has now secured music publishing and songwriting rights for all 161 of his songs, including some he co-wrote during his time in the 'Dreams' group.
What's more, Hipgnosis will also claim a 50 per cent share in any future releases by the 71-year-old songwriter.
As a solo artist, Lindsey has released six solo albums and three live albums.
In a statement, he said: “I was pleased to find a kindred spirit, someone who’s a big fan of my work in Fleetwood Mac, and an even bigger fan of my solo efforts.
“I look forward to working with Merck and the whole Hipgnosis team going into the future, and am confident that my body of work will be curated with great heart and insight."