President Mary McAleese and her husband Dr Martin McAleese will formally welcome the prince and Ms Wittstock at Aras an Uachtarain and will host a state dinner in his honour. The royal couple will also plant a tree in the grounds of the Aras before visiting the Garden of Remembrance in Dublin city centre.
During his visit, Prince Albert will attend events in Dublin and Galway, and will meet Taoiseach Enda Kenny at Government Buildings.
Officials said the programme for the prince's visit would reflect the long-standing ties between Ireland and Monaco and would underline the potential for future co-operation in areas of business, the environment, research, education, tourism and culture.
Prince Albert will also be accompanied by a delegation from the Monaco Chamber of Economic Development during certain events.
He will visit Trinity College Dublin and the city's docklands and will also inaugurate an exhibition in honour of Princess Grace at Farmleigh House, where he will host a reception to highlight Irish literature and art. The prince will visit the Irish Marine Institute in Oranmore, Co Galway.