After the ceremony, the newly inaugurated president will then travel to Áras an Uachtaráin, the official home of the Irish president, via motorcade.
A state reception will take place on Tuesday evening in Dublin Castle.
Connolly has served as a TD (member of Irish parliament) since 2016 and her election as president will trigger a by-election in Galway West.
She previously worked as a barrister and psychologist.
