She will start in July, replacing chairman Donald Brydon who temporarily took the top post after the departure of director Robert Pritchett in September last year.
Pritchett joined the charity when it was created in 2002 through the merger of the Christian Children's Fund of Great Britain and the European Children's Trust.
A spokesperson for Everychild said that Pritchett never intended to stay after consolidating the organisation post-merger.
At the Association of London Government, Feuchtwang has been involved in the work of the London Child Protection Committee and the campaign to end child poverty in the capital.
She was previously director of On the Line, a Millennium project founded and supported by Channel 4 newscaster Jon Snow. She was also head of communications at Oxfam for five years.