Capitalism is the best economic system for wealth creation, but it can come at a cost, according to U2 singer, social activist, and investor Bono.

"It's a wild beast, and if not tamed, can and has chewed up a lot of lives," Bono said in a CNBC interview from the World Economic Forum in Davos, Switzerland.

"Though it has taken more people out of extreme poverty that any other 'ism,' it's caused a lot of damage, a lot of harm," he said in the interview, which aired Thursday. "We need to re-imagine it, repurpose it, remake it, in our own image and the image of this new generation coming through that really, really want their world back."

To that end, Bono and private equity giant TPG are partnering on a new organization, called Y Analytics, to develop metrics for analyzing the impact of social and environmental investments. The goal is for economists and researchers to work with investors to make decisions that benefit society in addition to scoring high financial returns.

"Consumers are becoming aware they've got power in their pockets," Bono said. "They can close down companies, they can build them up. And I think it's sort of be on the train or be under it, really."

Bono and Bill McGlashan, founder of the TPG Growth platform, told "Squawk Box" co-host Andrew Ross Sorkin they want to bring new legitimacy to social impact investing.

"Impact historically was more of a good intention," said McGlashan. But Y Analytics aims to hold us accountable, "every day with every deal, in a way that allows us to, with substance, actually measure the output," he added.

McGlashan said Bono's input will enable TPG to deploy capital with equal emphasis on activism and investing in growing companies. Bono cited delivery drones in Rwanda as an investment with high financial and social returns.

"Everything I love comes together in that moment," Bono said. "I've seen at first hand what brutal, stupid poverty looks like. And so I can see that family that's transformed by that."

To reach the UN's sustainable development goals by 2030, the pair said the private sector will have to take a bigger role in activism. "It's just not going to be possible with public funds," Bono said. "We need public funds, but we're going to need the private sector, too."

That's in line with a trend Bono sees in consumerism in which millennials care more about ideas than about brands, and are loyal to environmentally and socially conscious companies. Millennials will "be calling us on whether we're firefighters or arsonists," he said. "And I think it demands us to ask hard questions of ourselves."

Y Analytics grew out of The Rise Fund, an impact investing fund co-founded by Bono and McGlashan in 2016 that has invested nearly $2 billion around the world.

The new organization will be headquartered in Washington and led by Maryanne Hancock, CEO of Rise Labs and a former senior partner at McKinsey & Co.

McGlushan said eventually, impact investing will just become investing. "Every investment has an impact," he argued. "The question is, is it a good impact, a bad impact, something in between?"