According to a tradition, Saint Helena, mother of the emperor Constantine discovered the cross of Jesus on September 14, 320 in Jerusalem. Then she commissioned the construction of the Holy Sepulcher Church over the place of crucifixion and resurrection on Golgotha (consecrated on September 13, 335). The feast of the cross (September 14) probably originated as a feast associated with the consecration of the Basilica: the church anniversary was complemented by public exposition of the cross for veneration on the next day.
The existence of the relict of the holy cross is only attested with certitude by Cyril from Jerusalem around 347/348. The pilgrim Egeria (381/384) reports about celebrations commemorating the consecration of the Resurrection- and Passion-Church, and also mentions the discovery of the cross. Her report, however, lacks any hint at the veneration of the cross.
The feast of the Exaltation of the Cross on September 14 spread first in the Christian East and it included reenactment of the elevation of the cross. The first testimonies from Rome come from the 7th century, where it competed with a similar feast celebrated on May 3. According to a legend of gallic origin, the cross was allegedly found already by pope Eusebius (309). The feast of the Discovery of the Holy Cross on May 3 known in the old Roman Missal was removed as late as 1960 by Pope John XXIII.
The current missal only has one feast of the exaltation of the Holy cross on September 14. The preface says:
you placed the salvation of the human race on the wood of the Cross, so that, where death arose, life might again spring forth and the evil one, who conquered on a tree, might likewise on a tree be conquered.Roman Missal, Preface