The regiment has strong links to the city as an Army Reserve unit is based in Raglan Barracks and the Freedom of Newport was granted to them in 1978.
They paraded through the city centre with colours flying, drums beating and bayonets fixed as they were led by the Band of the Royal Artillery.
The parade started at 12:30 BST.
It began on Cambrian Road before continuing on to Bridge Street and High Street to the D-Day Memorial where a short ceremony took place.
The parade then reformed and travelled down High Street, across Stow Hill and followed Commercial Street to its junction with Charles Street and Llanarth Street.

The Met said the "vast majority" of the work in its inquiry into Madeleine's disappearance had been completed.
It said no conclusion had been reached but it was now following a "small number of focused lines of inquiry" which was why the team had been cut.
Madeleine's parents said they "fully understand" the decision.
They said they remained "hopeful" their daughter would be found.
Madeleine, from Rothley in Leicestershire, was three years old when she went missing from her family's holiday apartment at the Ocean Club in Praia da Luz on 3 May 2007.
Assistant Commissioner Mark Rowley, from the Met, said: "The Met was asked to take on this exceptional case as one of national interest.
"We were happy to bring our expertise to bear only on the basis that it would not detract from the policing of London; and the Home Office have additionally funded the investigation above normal grants to the Met.
"That will continue at the reduced level."
Clickable map and timeline
Madeleine's parents Gerry and Kate McCann praised the "meticulous and painstaking work" done by police.
They said: "We are reassured that the investigation to find Madeleine has been significantly progressed and the Met has a much clearer picture of the events in Praia da Luz leading up to Madeleine's abduction in 2007.
"Given that the review phase of the investigation is essentially completed, we fully understand the reasons why the team is being reduced.
"We would also like to thank the Home Office for continuing to support the investigation.
"Whilst we do not know what happened to Madeleine, we remain hopeful that she may still be found given the ongoing lines of inquiry."
Detectives from the Met began working through material and following lines of inquiry after the Home Office requested a review of the case in May 2011.
Operation Grange, which has been supporting the Portuguese police's investigation, became a full investigation in July 2012.
Officers have now finished bringing together and investigating the information held by Portuguese police, the UK investigation and the private investigators working on behalf of the McCann family, the Met said.
1,338
statements taken
1,027
exhibits collected
60 persons of interest investigated
8,685 potential sightings considered
560 lines of inquiry identified
30 requests made to other countries asking for work to be carried out
The force said the inquiry had taken 1,338 statements and collected 1,027 exhibits but had not reached a conclusion yet.
Clarence Mitchell, spokesman for the McCanns, said: "Kate and Gerry are far from disillusioned. This is no way the end of Operation Grange.
"If anything it will now continue on a newly-focused, smaller yes, but focused basis that will hopefully lead to Madeleine being found somewhere in the near future."
Officers have investigated more than 60 persons of interest, the Met said, adding that a total of 650 sex offenders had also been considered as well as reports of 8,685 potential sightings of Madeleine around the world.
Having reviewed all of the documents, "7,154 actions were raised and 560 lines of inquiry identified", the Met said.
It said more than 30 requests had been made to "countries across the world asking for work to be undertaken on behalf of the Met".
About 100 soldiers from the 104th Regiment Royal Artillery marked their 50th anniversary with a freedom parade through Newport on Saturday.
[NEXT_CONCEPT]
The number of UK officers investigating the disappearance of Madeleine McCann has been cut from 29 to four, the Metropolitan Police says.