The pictures were taken when Stephen McGown arrived in South Africa on Sunday morning.
Thursday's briefing will be held at the Gift of the Givers' offices in Johannesburg.
McGown was released last week after his abduction from a hotel in Mali in 2011.
He was expected to address the media last week, but doctors asked him to delay the event.
The government says no ransom was paid to secure his release.
His captors were demanding millions of euros to set him free.