The late pop star held a 50 per cent stake in Sony ATV Music Publishing as part of a business partnership dating back to 1995.
The deal means Sony now has the rights to around three million songs, including works by The Beatles, Leonard Cohen, The Rolling Stones, Ed Sheeran and Taylor Swift.
The singer's estate will maintain holdings in Mijac Music, the owner of all of the songs he wrote, in addition to EMI Music Publishing.
Sony Corporation of America today signed a binding memorandum of understanding with the estate to obtain full ownership of Sony ATV Music Publishing.
Sony Corporation's president and chief executive Kazuo Hirai said: "The entertainment businesses have long been a core part of Sony and are a key driver of our future growth...
"This agreement further demonstrates Sony's commitment to the entertainment businesses and our firm belief that these businesses will continue to contribute to our success for years to come."
Michael Lynton, chief executive of Sony Entertainment, added: "This acquisition will enable Sony to more quickly adapt to changes in the music publishing business, while at the same time continuing to be an unparalleled leader in the industry and a treasured home for artists and writers."