It will also take on the Norwegian company's outstanding debt of $800 million.
Transocean said Aker Drilling’s board of directors had unanimously recommended shareholders accept the offer.
It added it had inked an irrevocable agreement with Aker Capital on Sunday to purchase 41% of the outstanding shares in Aker Drilling.
Transocean will acquire the shares held by Aker Capital's through the purchase of nearly 15 million shares by an affiliate company, representing 4.99% of the outstanding shares in Aker Drilling, and a pre-commitment agreement for the remaining 107.9 million shares, representing 36.1% of the outstanding shares, to be purchased by Transocean pursuant to the offer.
Including the shares to be acquired from Aker Capital, Transocean said it had already received consent for the deal from shareholders representing about 60.5% of the outstanding shares in Aker Drilling.
Transocean said it expected the deal to immediately increase earnings and for Aker Drilling to contribute about $1.05 billion in firm contract backlog.
Aker Drilling operates two harsh environment, ultra-deepwater, semi-submersible rigs which are currently on long term contracts with Statoil and Det Norske in Norway.
The company is also expected to take delivery of two sixth-generation drillships from South Korea’s Daewoo Shipbuilding & Marine Engineering in 2013.
Shares in Aker Drilling soared 97% early on Monday to Nkr26.30 per share, up from Friday's closing price of Nkr14.50 per share, on news of the takeover offer.