The switch came about due to “concerns over the quality of the playing surface” at the original venue.
City Stadium is the home of club side FK Sutjeska and regularly hosts Montenegro Under-21 matches.
The FAW and 700 travelling Wales fans, many of whom have already booked accommodation in the capital will have a journey of around an hour from Podgorica by road or train.
In a statement, external, the FAW added: “Since the change of venue, the FAW has been meeting daily with fan travel organisers, and with their collaboration and understanding, arrangements have been made to ensure Cymru fans with tickets will be able to attend the Nations League match on 9 September.
“The FAW has also been in communication with the Football Association of Montenegro and have confirmed that the original ticket allocation will be honoured. The FAW does not expect any additional tickets to be made available.”
The governing body earlier acknowledged “the inconvenience that this announcement will have on Cymru’s travelling fans, who have already planned for Podgorica”.
Chief executive Noel Mooney had also said the FAW had “been asking for a new pitch to be laid in Podgorica for several weeks”.
In a statement issued on its website, Uefa said “extremely hot conditions” in Montenegro this summer meant the pitch at Gradski Stadion in Podgorica had “suffered significant damage”.
The statement continued: “This combined with a heavy match schedule has meant that despite the best efforts of the Football Association of Montenegro to improve the quality of the pitch, the Nations League fixture between Montenegro and Wales will be moved to an alternative venue, City Stadium Niksic, to ensure a better pitch quality for the match.”
