Ackerman's base salary was $348,140 annually.
Neither Nutter nor School District officials would identify the donors of the $405,000, which is to be channeled through a district-affiliated charity, Philadelphia's Children First Fund.
The nonprofit was established in 2003 to support the district. Board members include Ackerman, SRC Chairman Robert L. Archie Jr., and Ackerman's deputy and now interim superintendent, Leroy Nunery II.
They sit on the board with some of the city's leading philanthropists, including Sheldon M. Bonovitz, chairman emeritus of Duane Morris - where Archie is a partner - and Harold Honickman, the soda magnate.
Nutter insisted that the district spend no more than $500,000 to satisfy Ackerman's buyout, sources said. The mayor said he supported the private fund-raising effort and personally solicited donations "because my interest was minimizing the number of public dollars."
Archie did not return calls seeking comment.
Rep. Mike McGeehan (D., Phila.), an Ackerman critic, asked state Attorney General Linda Kelly to determine the buyout's legality.
"That we have private-interest money mixing with public interest flies in the face of 40 years of progress on transparency," McGeehan said. "The dome of the Capitol should be blowing off and if it isn't, shame on them."
Federal tax law prohibits someone from taking a deduction for a donation earmarked for a specific person, said attorney Laura Solomon, whose Laura Solomon & Associates in Wynnewood works exclusively on nonprofit law.
It is possible, she said, to have one or more donors designate funds for a school district's use, adding, "There is absolutely a legal way to do this."
As long as the organization receiving the contribution is a public charity, as Philadelphia's Children First is, the donations can remain anonymous, she said.