The 15 oil rigs being acquired include Transocean's entire jackup fleet, which is comprised of 10 of Transocean's own rigs and five new rigs under construction, the press release said.
The estimated $1.35 billion price tag includes any remaining contract backlogs and yard installments, or any fees that would be required of the 5 rigs still under construction, Borr Drilling said.
"The potential purchase price ... suggests slight downside to [Transocean's] stock price," BMO Capital Markets analyst Dan Boyd told CNBC in an email. "I think some analysts grossly misinterpreted the news last week and did not account for the remaining new-build liability payments of more than $1.1 billion."
Boyd is referring to an article that surfaced last Friday, suggesting Borr was in talks to acquire the 15 rigs for $1.2 billion, according to an unnamed source who spoke to oil and gas news site Upstream Online.
Transocean still owes $1.1 billion in new-build payments on its rigs, according to BMO, and Boyd said he doubts Borr's acquisition price of the rigs includes the lingering liabilities, "as that would imply Borr paying full replacement cost."
Norway-based Borr said it has secured financing for the deal through a private placement of equity securities, and the acquisition should be completed before the end of May 2017.
The stock closed the day down 2 percent, hovering close to $12 per share.
Despite Monday's declines, shares of Transocean have risen more than 10 percent over the past 12 months and more than 30 percent over the past six months.