The 76 troops from 2 Company 1st Battalion Welsh Guards are representing the UK at the invitation of the Russian government.
They will march alongside more than 10,500 Russian soldiers and others from the US and France.
Some opponents of the Russian President Dmitry Medvedev are angry that foreign troops will take part in the parade.
“It’s a violation of tradition,” said Sergei Obukhov, a member of the Communist Party’s central committee.
“The presence of foreign troops with weapons in their hands is… an unnecessary reminder that we lost the Cold War.”
But Barack Obama, who is unable to attend the parade because of a scheduling clash, backed the decision to invite Nato troops.
The event also features a 1,000-strong military band, 161 tanks and missiles and 127 aircraft.
Six types of defence equipment will be on show during the hour-long parade as part of a display of military prowess expected to dominate Moscow’s sky and roads.
“There is a sense of pride to be in this massive parade on Red Square,” said Guardsman Ian Mundy, one of the British soldiers involved.
“It seems that everyone is interested in us as well and I’m proud to be a part of that.”
Lance Corporal John Sanigar added: “It’s a brilliant place to be at the moment for the Army and the Welsh Guards.”
The Welsh Guards served in Afghanistan six months ago and lost their commanding officer, Lieutenant Colonel Rupert Thorneloe, during the tour.
They are staying at the Moscow Military Academy as guests of the Russian Army and have been given a guided tour of the Kremlin and invited to cultural events.
Lieutenant Colonel Charlie Antelme, who took over as commanding officer after Lt Col Thorneloe’s death, said the parade would be a “surreal” experience.
“This is going to be a historic moment for the Welsh Guards and the British Army, and, of course, for the Russian people,” he said.
