The UN Human Rights Council has taken note that Alamuddin is unavailable to serve on the Gaza Commission of Inquiry due to her prior professional commitments.
In a statement on Tuesday, President of the UN Human Rights Council Baudelaire Ndog Ella said he "regrets" that the commission will not benefit from Alamuddin's expertise in the field.
The Council had announced that Alamuddin, professor of international criminal law William Schabas and Doudou Diene from Senegal, a United Nations Special Rapporteur on contemporary forms of racism, will form the independent Commission of Inquiry.
Ella said he had approached a number of individuals as potential candidates before issuing a statement that announced his decision to appoint three of them as commissioners.
Following the announcement on the panel, Alamuddin had said she was "unfortunately not in a position to accept this role."
Ella said the commission is now operational and he would "decide on the way forward and on how to best support and strengthen the Commission of Inquiry in its activities."
The panel would investigate purported violations of international humanitarian and human rights laws in the Occupied Palestinian Territory, including East Jerusalem, and particularly in the Gaza Strip since the conflict began on June 13.
London-based British-Lebanese Alamuddin, who is engaged to be married to Hollywood actor George Clooney, had said in a statement that while she was "honoured" to have received the UN offer, she would not be able to accept the role "given existing commitments -- including eight ongoing cases."
She said was "horrified" by the situation in the occupied Gaza Strip, particularly the civilian casualties that have been caused, and "strongly believe that there should be an independent investigation and accountability for crimes that have been committed."
Alamuddin specialises in international law and human rights and has worked at the International Court of Justice and as legal adviser to the Prosecutor of the Special Tribunal for Lebanon.
At least 1,948 Palestinians, the majority of them civilians, have been killed in the conflict, along with 67 Israelis, according to figures cited by the UN Office for the Coordination of Humanitarian Affairs.
The Council had decided, by a vote of 29 countries in favour, with 17 abstentions and a sole negative vote by the United States, to launch the inquiry at its emergency meeting in July.
Making sense of India's response to the Gaza crisis
Dialogue only option to resolve Gaza crisis: India
It's official! George Clooney, Amal post wedding banns
Why the Shiv Sena won't say sorry
Israel, Palestinians agree to another 72-hour ceasefire