Megan Bell from Seaham, near Sunderland, and Peter McCallum from Lochgilphead, who were both 17, died in separate incidents at the festival.
Mr McCallum was described by his family as a "kind and caring brother and son".
Miss Bell's family said her death would leave an "irreplaceable gap" in their lives and that she would be "so sadly missed".
Police Scotland said that both deaths were not being treated as suspicious and a report had been sent to the procurator fiscal.
Mr McCallum's family said in a statement: "Peter was a kind and caring brother and son.
"He was a talented singer who had ambitions to become an architect.
"We hope that people, especially the younger members of society, learn a lesson from Peter's death and that they don't put their families through the devastation we are experiencing just now."
Miss Bell's family said: "We are devastated at the tragic loss of our wonderful daughter Megan.
"Her death leaves an irreplaceable gap in our lives and she will be so sadly missed by all her family and friends.
"We would also like to thank everyone for the overwhelming number of flowers, cards and condolences sent to us as this very sad time."
The families of two teenagers who died at the T in the Park have spoken of their "devastation" over the tragedies.