Reports had linked Miller, who currently races for the Marc VDS Honda outfit, to the Ducati squad before the mid-season break, with his three-year contract with Honda set to expire at the end of the year.
The Australian's Suzuka 8 Hours commitments with the works Honda HARC-Pro team made an announcement impossible before the Japanese enduro took place at the end of last month.
Further negotiations then took place last weekend at Brno, where the final details of a one-year agreement were firmed up for Miller to join Danilo Petrucci at Pramac for 2018.
Miller's move was confirmed on Thursday evening ahead of this weekend's Red Bull Ring round in Austria.
He will take the place of Redding aboard Pramac's year-old Desmosedici machine, with Petrucci riding a latest-spec GP18, but will have a direct contract with Ducati.
Having lost his seat to Miller, Redding now faces an uncertain future.
A move back to Marc VDS with which he raced in 2015 is thought to be his best option of staying in the MotoGP paddock.
He has also been linked to a ride in World Superbikes with the privateer Barni Ducati squad, but said last weekend that staying in MotoGP remained his priority.