TED, the nonprofit known for its hugely popular video lectures—or TED Talks—and the TED Prize, which annually awarded $1 million to social entrepreneurs aspiring to solve global problems in health care, education and other areas, announced Wednesday the launch of a project that aims to take the group’s philanthropic impact to the next level.

The Audacious Project, which is backed by the collective investment of an influential group of foundations such as the Bill & Melinda Gates Foundation, grew out of and will replace the...