Its founders hope to "reimagine secondary schooling."
Building 21 will have no admissions criteria, and will keep 60 percent of its seats for neighborhood students. The rest of the student body will come from a citywide lottery.
Laura Shubilla, a Building 21 cofounder and a former chief executive of the Philadelphia Youth Network, said Tuesday that the PSP money would help pay for teacher training, building improvements, and other start-up costs.
"When the school is full, it will be sustainable on district revenue," Shubilla said.
Shubilla said she was gratified by PSP's investment and looking forward to bringing a new model to Philadelphia.
Applications for Building 21 and the two other new high schools, the U School and LINC, will be taken between March 24 and April 25.
PSP's next-largest grant, $575,000, will go to help New Foundations Charter School in Northeast Philadelphia expand.
The group will also give $88,000 to help a group of district and charter schools plan for regional collaboration in North Philadelphia. The group includes Aspira of Pennsylvania, Congreso de Latinos Unidos, Nueva Esperanza, Councilwoman Maria Quiñones-Sánchez, and the Philadelphia School District.
PSP will also grant $25,000 to Liguori Academy for planning a new, alternative Catholic high school for at-risk students.
The new school is seen as a second-chance opportunity for students in danger of failing out of traditional archdiocesan high schools.
Since its founding in 2010, PSP has spent $31.4 million on district, charter, and private schools in the city, most of which educate children from low-income households.