Despite fierce opposition from environmental and Aboriginal groups, legislation to create Australia's first nuclear waste dump has passed through the Senate.

The passage of the National Radioactive Waste Management Bill paves the way for a highly controversial plan to store nuclear waste at Muckaty Station, a remote Aboriginal community 120 kilometres from Tennant Creek in the Northern Territory.

The bill was passed after the Coalition did a deal with the government in February to establish a $10 million fund to be paid to the state or territory that accepts the facility.