WASHINGTON — Arne Duncan, the secretary of education, whose influential Race to the Top program offered financial incentives for school districts to innovate, announced Friday that he would step down in December, marking the departure of one of the longest-serving members of President Obama’s cabinet.

Mr. Duncan was arguably one of the most powerful education secretaries in history, both because of his personal ties to the president and the billions of dollars in funding that came to the department as part of the fiscal stimulus program during the financial crisis.

He was at times the subject of criticism from both parties, angering Democrats by challenging teachers’ unions and infuriating Republicans by promoting national academic standards.

Mr. Obama announced that he would nominate John B. King Jr., the deputy education secretary and a former commissioner of education in New York State, to replace Mr. Duncan.