The pair will share the nine million Swedish kronor (about $1.01 million or 860,000 euro) prize.
Romer, who is at the NYU Stern School of Business in NY, was honoured for his work on the role of technological change in economic growth.
Nordhaus, who has been called "the father of climate-change economics", developed models that suggest how governments can combat global warming. We look at the consequences of putting Nordhaus' research on the economic impact of climate change to policy.
New academic work is beginning to combine Romer's and Nordhaus' models by studying how investment in research and development can lead to new technologies that replace fossil fuels, for example.
William Nordhaus, one of two men to receive the Nobel prize in economics on Monday, grew up in Albuquerque and travels yearly to New Mexico for summer visits with family.
"This is, for sure, a Nobel Prize about the big questions", University of MI economist Justin Wolfers said on Twitter.
Hours before the award, the United Nations panel on climate changed warned of the risks of more frequent heatwaves, floods and drought in some regions as well as the loss of species without a radical rethink in how societies operate.More news: Xero champions mental health awareness and support in the workplace
Whether it's improving communication systems, developing new drugs, or coming up with potentially planet-saving environmental proposals, Romer argues that we can solve the world's most pressing problems with increasing speed using the principles of endogenous growth theory.
The Economics Nobel is only informally called so and is not technically a Nobel award.
"The second is how do we deal with the negative effects of economic growth, which have to do with the emission of greenhouse gases leading to a warmer climate - which not just hurts the economy, but risks the life of everyone on earth", Stromberg said.
Inspired by the acceleration in economic activity after the Industrial Revolution, Romer sought to explain how technological advances in the eighties drove economic growth. While handing over the honour to the Nobel Laureates, the Royal Swedish Academy claimed that both Nordhaus and Romer have come up with the methods that address some fundamental and alarming issues. An additional seven former MIT faculty have won the Nobel Prize in economic sciences.
Last year, the prize went to U.S. economist Richard Thaler, a co-founder of the so-called nudge theory, which shows how people can be persuaded to make decisions that leave them healthier and happier.
This year four other Nobel prizes were handed out - Arthur Ashkin, Gerard Mourou and Donna Strickland for Physics, Frances Arnold, George Smith and Gregory Winter for Chemistry, James P Allison and Tasuku Honjo for Medicine and Denis Mukwege and Nadia Murad for Peace. A total of 81 laureates have been named over the prize's 50 year history.