Sgt Joseph took on the task of Goat Major in 1977 - a role that involves looking after the wellbeing and upkeep of the Regimental Goat, carrying out ceremonial duties and attending various public and charitable events.
The most high profile of those outings over the years has been the appearances at the Welsh rugby internationals when, moments before kick off, he walks Shenkin the goat out in front of the Welsh rugby captain and the rest of the team.
It's a tradition which has endeared the Goat Major and Shenkin to the thousands watching in the stadium and also the watching millions on television.
"There's no doubt I'll miss the job," said David, (Joe the Goat to all who know him). "There are so many great memories of meeting so many different people.
"The noise of the crowd and the atmosphere is always very special."
One abiding memory is of meeting the Queen in 2006, at the National Museum in Cardiff, shortly after Her Majesty officially opened the Senedd, the Welsh Assembly building in Cardiff Bay.
"I'll never forget when the Queen stepped out of the car and asked, 'How are you David'," added David.
"I was taken aback that she called me by my first name. It was a really nice surprise."
Sergeant David Joseph joined the Welsh Regiment in May, 1969, signing up in Crickhowell, and following amalgamation with The 1st Battalion The South Wales Borderers the 1st Battalion The Royal Regiment of Wales 24th/41st then came into being. He has served in Northern Ireland, Germany and Hong Kong.
He joined the TA in 1994 after 25 years in the Regular Army and was appointed the Goat Major. Joe is married to Lorraine and dad to Lisa, Leanne and Sarah and lives in St Mellons, Cardiff. His day job is as storeman for C Company, working in Pontypridd.
The established practice of leading the Welsh rugby team out for Test matches now seems like a long-held tradition. However, it originated from a cheeky request in 1999 when Wales hosted England at Wembley, a location used while the final plinths of the Millennium Stadium were being polished prior to its gates being opened.
It remains an unforgettable match for Welsh fans who saw Scott Gibbs score a last-gasp try to nick the game from England.
"I remember that at some point before kick off I asked the team if I could lead them out and was told yes, so when the band were going through their final preparations I headed off the pitch towards the tunnel,
"I could hear the Drum Major or someone saying, where's he off to'? Next thing, they watched as I led the team onto the pitch. Ever since then I've continued to do it."
And it's this tradition which has enhanced the iconic status the Regimental Goat and Goat Major have in the public conscious, linked to both rugby match days and military parades.
But it's a more disciplined role than some people may think and isn't all about mingling with stars and being mobbed by fans down Westgate Street, hungry for a picture.
"This isn't a job where you can have weekends off - it's a 365-day thing. When Maindy Barracks is on stand down, for holidays such as Christmas, I still have to come in, feed the goat and make sure he's okay and looked after.
"I suppose my wife will be glad when I'm finished (Joe's last day will be on December 19, the day of his 59th birthday). The last time we really had a holiday was in the 1980s while I served in Hong Kong. We went to Phuket for a break."
In total, David has looked after five goats - two named Taffy during his time with the Royal Regiment of Wales and three named Shenkin while he's been with 3 Royal Welsh.
"Each goat has its own personality and some are better behaved than others," said Joe. This Shenkin is probably one of the best.
"But some of the real pleasures over the years have been to work with and support so many charitable causes - the Macmillan nurses and different other organisations. Dreamflight (a charity whose purpose is to send seriously ill children on the holiday of a lifetime) is also a cause where I've met so many celebrities - people like Sir Cliff Richard and Catherine Zeta Jones.
"Being involved in these kinds of things is rewarding and always interesting.
"I would like to thank my wife and family for putting up with my very busy life as Goat Major for all these years.
"It is a very demanding job but very rewarding and always interesting. I'm very proud to have been given the opportunity to serve as Goat Major."
Gareth Edwards, regarded by many as the greatest to have played the game, acknowledged Joe's iconic presence.
"He walks past me almost every game because I do interviews and make pre-match presentations in that area," said the Welsh rugby legend.
"He's very much part of the occasion and I think it's wonderful and the crowd appreciate them because they're that popular."
Gareth joked: "I've seen Joe regularly tow the goat along but I know the goat is towing Joe along.
"I'm sure Joe will have gathered some great memories. We will certainly miss him because he's very much part of the Arms Park experience. I'm pleased to wish him all the best."
Lieutenant Colonel Jeff Cleverly, Commanding Officer 3rd Battalion The Royal Welsh, said Joe's dedication to the role was exceptional.
He said: "What has stood Sgt Joseph out from his peers in the other two battalions is his understanding and respect for the high profile role he fulfils.
"His bearing, manner and sheer presence adds tremendous value to each occasion and his intuitive feel for public relations ensures that the Army and the regiment are always shown in a positive light.
"The dedication shown by Sgt Joseph in his support to community engagement and the promotion of the Army in society has been exceptional.
"As a result, he has become an iconic figure in Wales and an outstanding ambassador. He has paraded at numerous fixtures in support of both the military and civilian organisations and he has been seen at some of the most high profile events within Wales.
"He works tirelessly in support of a wide range of charities, often completing up to seven engagements on a single weekend. He has supported a diverse range of charities, including Help for Heroes, the ABF and the British Heart Foundation.
"However, he has focussed the majority of his effort into the support of children's charities. These have included national, regional and local institutions. He has particularly strong links with the Noah's Ark Appeal, Ty Hafan and Dreamflight.
"It is impossible to overstate the positive impact that he has made to both the standing of the Army in Wales and the charities that he supports and still, he approaches each engagement with the same high level of zeal and enthusiasm.
"His unwavering dedication to his role and his tireless charity work over this length of time is nothing short of remarkable."