Shortly after 1100 BST on Monday, the C-17 Globemaster transporting the the bodies of Col Thorneloe and Trooper Hammond landed at the RAF base.
The families of the two men said their own private goodbyes during a memorial at a chapel on the site, before the cortege proceeded to Wootton Bassett.
Later, hundreds of British Legion veterans, shopkeepers and local residents stood in silence as the cars carrying the Union flag-draped coffins slowly drove along the high street.
After pausing at the town's war memorial, the bodies were taken to Oxford's John Radcliffe Hospital for a post-mortem examination.
Maurice Baker, president of the Royal British Legion Wootton Bassett branch, said: "This is a military town, there's a lot of servicemen, so it's important to a lot of people here to pay their respects."
Wilbur Heynes, a cousin of Col Thorneloe, said the respect shown by the town had been "touching".
The bodies were flown into RAF Lyneham airbase.
He said the loss to his family had been "tremendously difficult".
He added: "A loss like this is terribly blunt, when someone leaves the world so abruptly."
More than 40 members of Trooper Hammond's regiment, dressed in their working uniforms of black overalls, also lined the street to pay their respects.
Sgt Maj Kevin McGarry, of 2nd Royal Tank Regiment, said Trooper Hammond's death had been difficult for his regiment.
"We're a family regiment. If you sign up for 22 years, you stay in the regiment for 22 years - everyone knows everyone."
BBC defence correspondent Caroline Wyatt said the head of the Army, General Sir Richard Dannatt, a personal friend of Col Thorneloe, was in Wootton Bassett to pay tribute to "the best of the best".
Col Thorneloe, from Kirtlington, near Oxford, of the 1st Battalion Welsh Guards in Aldershot, and Trooper Hammond, from Plymouth, of 2nd Royal Tank Regiment, were travelling as part of a resupply convoy when a bomb blew up their armoured vehicle on Wednesday.
Six other soldiers were injured in the blast near Lashkar Gah in Helmand province.
UK CASUALTIES IN AFGHANISTAN
Lt Col Rupert Thornoloe and Trooper Joshua Hammond
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.