Shares in the group, which has a vision of kickstarting the next wave of smart robotics, jumped more than 7.5 per cent to their highest point in nearly two decades on the news.
Boston Dynamics, which was bought by Google in 2013, is known for its eerily human and animal-like robots like Atlas and BigDog.
However, the group has had a tough time commercialising its robots, and Google put it up for sale more than a year ago.
As part of the transaction, SoftBank also agreed to acquire Japanese bipedal robotics company Schaft.
“Today, there are many issues we still cannot solve by ourselves with human capabilities. Smart robotics are going to be a key driver of the next stage of the Information Revolution, and Marc and his team at Boston Dynamics are the clear technology leaders in advanced dynamic robots," said Masayoshi Son, chairman and chief executive of SoftBank.
The boss and founder of Boston Dynamics, Marc Raibert, said the firm was excited to be part of SoftBank's "bold vision" and its part in the next technology revolution.
“We share SoftBank's belief that advances in technology should be for the benefit of humanity. We look forward to working with SoftBank in our mission to push the boundaries of what advanced robots can do and to create useful applications in a smarter and more connected world."