The Japanese investment giant will also pay $3 billion annually to use OpenAI's technology across SoftBank group companies.
The joint venture, SB OpenAI Japan, will be owned by OpenAI and a company established by SoftBank and its domestic telecoms arm.
Son is moving to deepen his exposure to OpenAI, with SoftBank looking at investing $15 billion to $25 billion in the company, Reuters reported last week.
SoftBank is also committing $15 billion to Stargate, a joint venture with OpenAI and Oracle (ORCL.N) to build AI capacity in the U.S., Reuters has reported.
The Stargate launch last month saw Son make his second appearance with Donald Trump since his election as president in November.
Son's backing for OpenAI reflects his reemergence as an investment force after a period of retrenchment sparked by the falling value of SoftBank's tech portfolio and a series of high profile stumbles.
He has a long history of partnering with tech firms in the U.S., with SoftBank bringing the iPhone to Japan in 2008.
