Extinction Rebellion (XR) Scotland has said three of its members had climbed aboard the Valaris 122 rig and intended to there for as long as possible to prevent it from operating.
The environmental group added that the trio had taken all necessary safety precautions and informed police of their “peaceful occupation”.
The rig is currently at Princess Alexandra Wharf at the Port of Dundee and is due to begin a nine-month contract for Shell later this month.
An XR Scotland spokesperson said protesters have been equipped with supplies and plan to hang an XR flag from the rig.
Activists have also urged politicians to decommission fossil fuel infrastructure, introduce a “just transition” for workers and communities, and establish a legally binding citizens’ assembly for environmental issues.
One of the members who boarded the rig, Jo, who declined to give her full name, said she was taking part in the protest for her niece.
“I don’t want to say to her that I didn’t take a stand when I had the choice and left it to other people to sort it out,” she said.
“I am going to give it my best shot and go down fighting because I can see the world through her eyes and I want to protect things for her.”
A fellow protester, Fiona, said the world has “zero chance” of staying below the 2C global warming limit set by the Paris climate agreement with the current size of the fossil fuel industry.
“We are currently living in a world warmed by 1.1C – and we are seeing the catastrophic, heartbreaking and devastating effects every day,” she said.
A spokesperson for Forth Ports, the owner of the Port of Dundee, said they are aware of the protest and have a pilot boat at the scene as a “safety precaution should anyone require assistance”.
Shell said it is aware of the incident and its “prime concern” is the safety of the workers and protesters involved.
Additional reporting by PA