The first, from 1st Battalion Coldstream Guards, died in an explosion in the Babaji area of Helmand province.
The second, from 1st Battalion Scots Guards, was shot fighting rebels in the Nad Ali area of the province.
Three Britons have died on Operation Moshtarak, and a total of 263 military personnel in Afghanistan since 2001.
The next of kin of both soldiers have been informed.
Spokesman for Task Force Helmand, Lt Col David Wakefield, said the first soldier, who was serving as part of Combined Force Nahr-e Saraj (South), had been involved in an operation to clear insurgents from the Babaji area.
This was so a checkpoint could be built and a road laid through the area.
“He died in the course of his duty and among his comrades. His courage and sacrifice will be remembered,” Lt Col Wakefield said.
He said the soldier from 1st Battalion Scots Guards, part of the 1 Grenadier Guards Battle Group, was shot fighting insurgents on Thursday afternoon.
“He died a soldier taking the fight to insurgents. He’ll be sorely missed but he will not be forgotten,” he said.
Operation Moshtarak is the biggest military offensive in Afghanistan since the Taliban were overthrown in 2001 and involves 4,000 British troops.
In total, more than 15,000 US, British and Afghan soldiers have embarked on a push to clear Taliban forces from Marjah and Nad Ali, in the southern province of Helmand.
The first British soldier involved in the offensive to be killed was Lance Sergeant Dave Greenhalgh.
The 25-year-old from Ilkeston, Derbyshire, who was serving with 1st Battalion Grenadier Guards, died in an explosion while on vehicle patrol near Lashkar Gah, in Helmand, on Saturday.
News of the latest death came on the day the bodies of L/Sgt Greenhalgh and four other British soldiers killed in Afghanistan were flown to RAF Lyneham, in Wiltshire.
The others were Lance Corporal Darren Hicks, Kingsman Sean Dawson, Rifleman Mark Marshall and Sapper Guy Mellors, who were killed in separate incidents in Helmand earlier this month.