Captain Walter Barrie was playing in a match on Sunday between British soldiers and members of the Afghan National Army at his base when he was shot at close range in the Nad-e Ali district of Helmand province.
News of the killing came after the Queen led the nation in honouring the fallen, as the country fell silent to remember its war dead.
The 41-year-old, from Lanark, has been hailed as a "great man" by his wife, Sonia. He also leaves his 15-year-old son, Callum.
His body was flown into RAF Brize Norton in Oxfordshire, where the Union Flag-draped coffin was carried with full military honours.
A private service was held for his family before a ceremony at the memorial garden on the outskirts of Carterton.
Members of the public and the Royal British Legion joined Capt Barrie's colleagues from the Royal Regiment of Scotland while a bell tolled as the cortege approached.
Royal British Legion standard-bearers slowly lowered their flags as the servicemen saluted their fallen comrade. As the cortege pulled away there was a round of applause.
Major Jimmy Law, of the Royal Regiment of Scotland, said: "Walter Barrie was professional, diligent and more importantly, he was just a brilliant bloke, with a great family. He loved his Glasgow Rangers Football Club, and he was really like a soldiers' soldier.
"All the blokes respected him and he really added a great deal of value every day, he was 100% professional."
Capt Barrie's wife said in statement: "He was a great man, a doting and amazing father and a fantastic husband. He will be missed by many."
Cpt Walter Barrie's body returned to the UK