Staff Sgt Schmid was serving with the Royal Logistic Corps Explosive Ordnance Disposal Regiment, based in Didcot, Oxfordshire.
He was a week away from seeing his family again when he was killed on Saturday in Helmand province.
He had been in the Army for 13 years and was commanding a bomb disposal team dealing with a roadside device near Sangin.
He was killed when the bomb went off as he was defusing it.
'Preserve life'
After the repatriation, Mrs Schmid said: "It's an emotional day but I'm very, very pleased to have my husband home.
"He's an absolute hero. It was awesome to see that plane coming in and witness him being taken off by his friends and those who loved him.
"He was a very unique, special man, very brave, there is no other man above him and I'm so proud of him."
Staff Sgt Olaf Schmid served in the Army for 13 years
Sgt Schmid was always prepared to take a risk, his brother Torben said.
"His mindset was that of the man who would go out and preserve life," Mr Schmid said.
Lt Col Robert Thomson, commanding officer of 2 Rifles Battle Group, said: "Staff Sgt Oz Schmid was simply the bravest and most courageous man I have ever met.
"No matter how difficult or lethal the task which lay in front of us, he was the man who only saw solutions."
Lt Col Gareth Bex, commanding officer of the counter IED (improvised explosive devices) task force, said Staff Sgt Schmid had been a "legend".
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