The bomb struck during a live interview
Mr Reeve was being interviewed live on BBC World television by fellow correspondent Lyse Doucet, when a 2,000 pound bomb smashed into a building about 50 metres away.
Viewers watching the interview heard the sound of the approaching bomb and as it exploded saw Mr Reeve diving to the floor, as a nearby wall collapsed.
Speaking in an interview with BBC News 24 on Tuesday, Mr Reeve explained that before the attack he had covered the windows of the office with plastic sheeting and that this had undoubtedly saved his life.
"The glass would have smashed into the back of my bald head and it would have been in particularly bad shape," he said by videophone.
Fear of more attacks
The bomb hit at 1745 (1315 GMT), blowing out all of the windows of the BBC office.
Mr Reeve immediately dived to the floor and urged his cameraman to head down into the building's basement.
Fearing more attacks he and the BBC's other Kabul staff swiftly left the area, taking refuge at a hotel for the night, only returning the next morning.
"We left pretty quickly because we were worried that there would be another bomb in the area. We've just got back to the office and all of the windows are shattered," he said.
Journalists killed
On Monday three journalists - two French and one German - were killed in northern Afghanistan in a Taleban ambush on an opposition convoy.
They were among a group travelling on an armoured personnel carrier (APC) with the Northern Alliance forces across the front line near the Tajik border.
An Afghan translator who was with the journalists is reported to be missing. An American journalist was injured.
They were the first media casualties reported since the US-led attacks in Afghanistan began last month.