The Japanese company made the announcement in a statement Thursday, citing more than 1 trillion yen of non-operating losses from investments held outside of its $100 billion Vision Fund.
The buyback tops the $20 billion in purchases sought by activist hedge fund Elliott Management
SoftBank shares fell as much 9.6% to a 14-month low on Friday amid a crash in global stock markets, but pared losses to close down 5% in Tokyo.
SoftBank owns 26% of China's Alibaba, with its origin in a $20 million investment in 2000, and the stake is now worth more than the Japanese firm's market capitalization
The tie-up would allow the companies to share SoftBank and Yahoo Japan's customer base and data analysis abilities with Aeon's wide product range and distribution network