Ms Verwoerd was dismissed last July as the UN agency was unhappy with the publicity she attracted following the death of the RTÉ figure.
Ms Verwoerd said she was shocked at the decision to terminate her position as executive director in Ireland with Unicef.
She pointed to her success as head of Unicef in this country. During her tenure, she had raised Irish funds for Unicef from €4.3 million to €8.4m in the period 2009 to 2011.
Mr Power served as junior minister in the Department of Foreign Affairs between 2008 and 2011, with responsibility for managing the government African Aid programme, which is based in Limerick.
Before entering the Dáil in 2002, Mr Power, who is a solicitor, worked with the Limerick law firm Holmes O’Malley Sexton.
Aged 47, he is married with four children.
As he progressed his political career from a seat on Limerick City Council to a junior government post, he encountered fierce rivalry from Willie O’Dea.
Mr Power, who was appointed a junior minister by Bertie Ahern, earned plaudits for his work on Africa Aid and made many contacts in various counties and within the UN.
Anther Limerick TD, Labour’s Jan O’Sullivan, has taken charge of the Limerick-based department since the general election.