Cpl Bryan Budd, 29, from Ripon, North Yorkshire, was killed in Helmand province at about noon local time (0830 BST), the Ministry of Defence said.
He was serving with the 3rd Battalion of the Parachute Regiment.
"[Cpl Budd] died as a result of injuries sustained during the contact. Three other British soldiers received minor injuries," an MoD spokesman said.
Twenty UK armed forces personnel have died in Afghanistan since 2001.
Softly spoken
Cpl Budd was married to Lorena and had a two-year-old daughter, Isabelle. Lorena is expecting a second child in September.
The MoD said Cpl Budd was softly spoken and a calm character whose "keenest passion" was his wife and daughter.
He was described as a shining example to those under his command, with great courage and a quick sense of humour.
He had been in the Army for 10 years serving in Yugoslavia, Sierra Leone, Macedonia, Afghanistan and Iraq. He was about to be promoted to platoon sergeant when he died.
Bryan died doing the job he loved, leading his men from the front - where he always was
Lt Col Stuart Tootal, CO
His commanding officer, Lieutenant Colonel Stuart Tootal, said he was a natural leader.
"Cpl Bryan Budd was an outstanding young man who had quickly risen through the ranks in the regiment.
"Bryan died doing the job he loved, leading his men from the front - where he always was.
"Bryan was proud to call himself a paratrooper and we were proud to stand beside him."
Persistent attacks
The 3rd Battalion, the Parachute Regiment, is based at Colchester Garrison in Essex.
Earlier, Defence Secretary Des Browne offered his condolences to the family and friends of Cpl Budd.
Three other British soldiers received minor injuries in the incident. Cpl Budd's death brings the number of British forces personnel who have died in Afghanistan since the start of operations in November 2001 to 20.
He is the latest victim of persistent attacks on British troops who are in Afghanistan to help rebuilding and to tackle terrorism and heroin cultivation.
They were serving as part of a multinational Nato force in the lawless south of the country.
Afghanistan is going through its bloodiest period since the fall of the Taleban five years ago. Much of the fighting has been concentrated in the south.
'Drawn into fights'
BBC world affairs correspondent Roland Buerk said the British Army and its coalition allies were trying to bring security to entire districts in Afghanistan.
"The plan was to make major centres safe, to bring in economic development, and hope to turn the local people away from whatever loyalty they had to the Taleban," he said.
"But it's just not worked out like that. They've been drawn to fighting in remote districts and they've been taking casualties."
Helmand, in the southwest of the country and Afghanistan's top opium producer, sees regular deadly violence blamed on Taleban fighters or drug lords.
Although the Taleban were ousted from power five years ago, supporters have this year stepped up attacks on foreign and Afghan troops.
The Ministry of Defence has tonight confirmed that a British soldier has been killed whilst fighting with insurgents in southern Afghanistan. 

The unnamed troop was killed in a gun battle with Taleban forces in the volatile Helmand province at around midday local time. 

A spokesman from the Ministry of Defence said: “The soldier died as a result of injuries sustained during the contact. Three other British soldiers received minor injuries.” The MoD also said that they are in the process of informing the soldier’s family about his death.

Defence Secretary Des Browne said: "I was deeply saddened to be informed of the death today of a British soldier and the injuries of three others as they supported the NATO mission in Afghanistan," he said. "I wish to express my sincere condolences to their families and friends. My thoughts are with them at this difficult time."

So far, twenty British armed forces personnel have died in Afghanistan.

Today, it has been reported that around seventy Taleban fighters were killed when they clashed with Afghan security forces and Nato-led troops.