Original: They were designed  by the American architects Philip Johnson and John Burgee, built by Fomento de Construcciones y ContratasFCC history and commissioned in 1996 by the Kuwait Investment Office (hence their initial name "Torres KIO" or "KIO Towers").
Simplified: They were built in 1996 by the Kuwait Investments Office (KIO) now owned by Caja Madrid and Realia Bussines.