King Charles III will attend Parliament to deliver the speech outlining the government's agenda.
The passengers and crew will have spent 72-hours isolating at Arrowe Park Hospital in Merseyside.
Ap Iorwerth said it was "the greatest privilege" after he became first minister of Wales on Tuesday.
Some farmers fear the reintroduction of the UK's biggest bird of prey will threaten their livestock.
More than 40 nations are involved in the mission, which the Ministry of Defence says will begin when conditions allow.