The new joint venture, Aker BP, will merge oil company Det norske oljeselskap, in which Aker is the biggest owner, and BP's Norwegian unit.
Aker will own a 40 percent stake and BP a 30 percent stake in the new company. The remaining shares will be held by other Det norske shareholders.
BP said it will also receive a cash payment of $140 million plus positive working capital adjustments as part of the deal, which is subject to approval by Norwegian and European Union authorities.
"The Norwegian Continental Shelf represents a significant opportunity going forward and we are looking forward to working together with Aker to unlock the long term value of the company through growth and efficient operations," BP Chief Executive Bob Dudley said.