George Connor Forester, 17, of Tudor Close, Chippenham, died in hospital early on Saturday.
A Renault Clio hit a tree on the A342, near the entrance to Rowdeford School, at about 0130 GMT on Friday.
Frankie Bowyer, 16, of St Teresa's Drive, Chippenham, died at the scene. Jamie Thomas Walker, 17, of Hatherell Road, Chippenham, died in hospital.
The male driver, 20, was not badly hurt, but was taken to hospital complaining of chest pain.
Wiltshire Police said he provided a negative breath test, but suffered minor injuries and was treated for extreme shock.
A statement from the family of Frankie Bowyer said he was a "dearly beloved boy".
The statement said: "Frankie lived life to the full. A popular friend to all that knew him, he will be sorely missed by his family and friends."