Dr Sellers, originally from Crowborough in East Sussex, is the deputy director of Nasa's science and exploration division.
The 60-year-old was diagnosed with stage four pancreatic cancer in late October.
"It did motivate me to concentrate my thoughts," he told the BBC.
"I'd been feeling rough for about six or nine months, getting progressively more ill.
"The outlook in terms of expected longevity was a bit of a shocker.
He has written an article for the New York Times in which he shares his thoughts on climate change.
He said: "I could look down and I could see cities and rivers and ship wakes and aircraft contrails.
"It's a very small world and it's pretty much all we've got.
"Leaving the home planet, looking back and then coming back again made me realise this is home."
Dr Sellers said he planned to continue his work which includes research into climate change "for as long as possible".
"I ended the article with a statement that given all the things that need to be done 'I'm going to work tomorrow'.
"Work is fascinating - I love the office, whether it is in a space suit or in a real office - I've always loved work.
"I'm trying to work 20 times the normal speed to get the work done."
Speaking of his diagnosis and treatment, Dr Sellers said: "The prognosis right now is 12 to 18 months."
Dr John Weeds, headmaster of Dr Sellers' former school in Cranbrook said: "It's really tragic. Piers has been and remains a very great ambassador for this school.
"He has made an enormous contribution to his field of science.  We are absolutely devastated by the news."
Dr Sellers had to become a US citizen to fulfil his dream of becoming an astronaut and has campaigned for the British government to develop its own space programme.
He said he was "delighted" when Tim Peake, who regarded Dr Sellers as a role model, arrived at the International Space Station with a British flag on his shoulder last month.
Dr Sellers said he still wanted to influence young people to enjoy science and work to combat climate change.
"I have no pretentions about leaving a legacy. I will leave other people to write that."
British-born astronaut Piers Sellers says he is now living life at "20 times normal speed" after being diagnosed with terminal cancer.