Craftsman Andrew Found, 27, of the Royal Electrical and Mechanical Engineers, died in an explosion in the Gereshk Valley area on Thursday.
Corporal Lloyd Newell, from the Parachute Regiment, was killed by small arms fire in a separate incident on the same day.
A third British soldier was shot while on patrol in Afghanistan’s Helmand Province on Saturday and has died of his injuries
The serviceman, from the 3rd Battalion The Mercian Regiment (Staffords), was in the southern Nahr-e Saraj district with the Afghan National Army when he came under fire.
Next of kin have been informed.
The soldier had been been sent from his base in Khar Nikar on a patrol with the Afghan troops.
He was shot at by insurgents and fatally wounded while standing guard.
The Ministry of Defence said father of two Craftsman Found died trying to rescue a vehicle which had been hit by another blast.
His wife Samantha Found said: “You’re my husband, my best friend and are my world. I cannot explain my pain and the hole you have left in all our lives. You are the best husband anyone could have wished for; a great dad, friend and you have touched the hearts of many in your life.
“You loved your job, your family and friends and always loved a good joke. You always made me smile. I will love you always and forever. You where my rock and my hero and always will be. I love you so much.”
The couple had a son, Jaxson. Craftsman Found also had another son Michael from a previous relationship.
His parents Jennifer and Alan Found and his brother Simon Found said: “Andrew died doing the job he loved. Even though we are all in pain now, we will remember the fun, the laughter and all the love he brought to all the people he knew and loved.”
Lieutenant Colonel Jonathan Biggart MBE called him a “an intelligent, selfless and brave soldier”.
He said: “Craftsman Found was killed by the blast of an Improvised Explosive Device while doing the job he loved and was so very good at. He was coming to the rescue of his Squadron comrades to recover a Warthog Armoured Vehicle damaged in an earlier blast.
“Right up until his final moments, the example he set, together with his wit, kept his fellow soldiers going under very difficult and demanding conditions.”
Major Jonathan Williamson said: “He was a true character, never afraid to make his opinions known. He was mature, a dedicated family man, and when he spoke it was worth listening.”
Cpl Newell’s age and where he was from were not released by the MoD. According to The Sun newspaper he was in the SAS.
An MoD spokesman said: “We cannot comment on Special Forces matters.”
An Army spokesman said: “Cpl Lloyd Newell was a man of integrity and principle. He was a natural and talented soldier who loved his work and the military lifestyle.
“He personified the great British Paratrooper - selfless, humble, cheerful and utterly reliable. He did his duty, relishing discomfort as a personal test, and always acting in the greater interests of the team.
“He attracted friends easily and cared deeply for those around him. His friendship was cherished by all.
“He was devoted to his wife and their nine week old daughter. Their family unit had the strength born of true love and kinship. Their loss is unimaginable.
“His vitality was palpable, his dignity natural, his humour refreshing. We salute him.
“The family have asked that their privacy is respected.”
The latest fatality brings the total number of UK troops who have died since operations in Afghanistan began in 2001 to 374.