Andrew and Julie Hore, who are organising the event, had hoped to enlist 258 motorbike riders to each carry a poppy cross bearing the name of a British life lost in the conflict.
But after word spread on social media, about 600 said they wanted to join in.
Those taking part on Sunday will donate Â£5 towards a memorial bench and stone.
They will then be placed in the Peace Gardens in Brecon.
Mr Hore said they had been keen to mark the anniversary of the end of the conflict as a number of bikers were ex-veterans.
Some 255 British military personnel and three Falkland islanders died during the war, which ended on 14 June 1982 when Britain accepted the Argentine surrender.
Of those who died, 48 were Welsh Guardsman and a further 97 were wounded.
"We are expecting hundreds and hundreds of people - lots of biking groups are coming together," said Mr Hore.
"We wanted a memorial to the soldiers in Brecon as there's not one here and we felt there should be one."
The bikers will leave Brecon at 11:00 BST on Sunday and will travel to the Falklands National Monument in Cathays Park, Cardiff, accompanied by the Wreath of Respect, a hand-made wreath of metal poppies.
They will then take part in a service to remember the conflict and will be joined by First Minister Carwyn Jones and other dignitaries.
A number of veterans and family members of those who died in the Falklands are also due to attend and lay crosses, including a woman who was just six months old when her father was killed.
Any surplus donations raised during the motorbike ride will be divided between the South Atlantic Medal Association and the Royal British Legion.
The Wreath of Respect, a project set up on 2014, has travelled around the UK and overseas, where it is laid at memorials and sites connected to the military.
Events have been held around the country to mark the Falklands anniversary, including at the Senedd in Cardiff Bay, where a ceremony on Wednesday was organised by the assembly's Armed Forces and Cadets cross party group and officers from the 160th Brigade (Brecon).
Hundreds of bikers are expected to ride from Brecon to Cardiff to commemorate the 35th anniversary of the Falklands War.