Sgt Gareth Thursby, 29, and Pte Thomas Wroe, 18, both of 3rd Battalion, The Yorkshire Regiment, were killed in Helmand's Nahr-e Saraj district. It is understood that the killer lured them to his side with a fake injury before firing on them.
Sgt Thursby, from Skipton, a father of two, was promoted to sergeant in 2010, having previously served in Kosovo and Iraq. His commanding officer, Lt Col Zachary Stenning, said: "I heard just a few weeks ago that he had told his platoon to call him Dad during the tour. That is how he saw himself - a father figure for 30 men and women involved in gruelling operations in Helmand."
Sgt Thursby's wife Louise described her husband as "our hero". "He was an amazing husband and father, happy, full of life and kind-hearted with a passion for his work and family," she said.
Pte Wroe, from Holmfirth, who joined the Army in 2010, was deployed to Afghanistan in July. His company commander, Maj Finlay Bibby, said: "He was an extremely talented soldier who was fulfilling his dream by serving with the battalion on operations, the same battalion that his father served with."
Pte Wroe's family said in a statement: "Our son Thomas was a brave young soldier, who is loved by his family, girlfriend and friends. We can't believe you have been taken so soon from us. You will always be in our hearts for ever and ever."
The Ministry of Defence said an investigation was under way into the circumstances of the soldiers' deaths.
Defence Secretary Philip Hammond said: "I was saddened to hear of this cowardly act by a man wearing an Afghan local police uniform, which has taken the lives of two brave British soldiers. All of our thoughts are with the families of Sergeant Gareth Thursby and Private Thomas Wroe. They gave their lives protecting Britain's national security, helping to make sure that Afghanistan never again becomes a haven for international terrorism."
Their deaths take the total of British military personnel killed in Afghanistan to 430 since operations began 2001.