UN Secretary-General Annan approved Eckhard's resignation on condition that he stay in service until June, said Aljazeera's New York correspondent, Ismail Baha al-Din.
Baha al-Din said Eckhard had tendered his resignation much earlier but it was only made public by Annan on Friday.
Eckhard, highly respected by the UN press corps, is 61 and the usual retirement age at the organisation is 60.
Eckhard has been an associate spokesman for secretaries-general over the past decade. He also served as a spokesman for peacekeeping when Annan headed that department shortly before he became secretary-general.
In a related development, Annan recently appointed Mark Malloch Brown, the high-profile head of the UN Development Program (UNDP), to be his new chief of staff.
The announcement comes as the UN is embroiled in allegations of sexual harassment against Ruud Lubbers, UN High Commissioner for Refugees Affairs.
Lubbers (C) may soon resign
after mounting allegations
Lubbers on Friday said he was "friendly to women" but denied allegations of sexual harassment that have added to the woes of the scandal-plagued United Nations.
Lubbers said he would not resign.
Lubbers demonstrated on a journalist how he said he had escorted a woman out of a meeting at his Geneva headquarters, which led to the initial harassment allegation last year.
"I ushered the lady out of the room with my hand on her back. And that was all," said Lubbers. "You could call it familiar but certainly not sexual harassment."
He added: "I might be friendly to women," but said that was a sign of good "gentlemanship".
He said he had spoken only "shortly" with Annan about the issue, but Annan's office issued a statement saying that the "main focus was Mr Lubbers' future in the organisation, particularly in light of recent developments - including today's press coverage".
Insiders said Lubbers would have to answer charges about his behaviour in the coming weeks.