His wife said: "Gareth was the love of my life. He was an amazing husband and father, happy, full of life and kind hearted with a passion for his work and family. He was brave, hard working, a loving husband who was a devoted father to his children. Our hero."
Pte Wroe was deployed to Afghanistan on July 1, shortly after his 18th birthday. He is survived by his parents, Michael and Claire, and sister Demi, from Holmfirth, West Yorkshire.
His 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.
"You would light up the room with your smile and bubbly personality. Our world will be a duller place without you. We are so proud of you son, on all you achieved and we are grateful for every special thing you gave us. We will always love you Tom."
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."