Telesphorus is traditionally reckoned as being the seventh Roman bishop in succession after Saint Peter. The Liber Pontificalis mentions that he had been an anchorite (or hermit) monk prior to assuming office. According to the testimony of Irenæus (Against Heresies III.3.3), he suffered a "glorious" martyrdom. Although most early popes are called martyrs by sources such as the Liber Pontificalis, Telesphorus is the first to whom Ireneaus, writing considerably earlier, gives this title.
Eusebius (Church History iv.7; iv.14) places the beginning of his pontificate in the twelfth year of the reign of Emperor Hadrian (128–129) and gives the date of his death as being in the first year of the reign of Antoninus Pius (138–139).
In Roman Martyrology, his feast is celebrated on 5 January; the Greek Church celebrates it on 22 February.
The tradition of Christmas Midnight Masses, the celebration of Easter on Sundays, the keeping of a seven-week Lent before Easter and the singing of the Gloria are usually attributed to his pontificate, but some historians doubt that such attributions are accurate.
A fragment of a letter from Irenæus to Pope Victor I during the Easter controversy in the late 2nd century, also preserved by Eusebius, testifies that Telesphorus was one of the Roman bishops who always celebrated Easter on Sunday, rather than on other days of the week according to the calculation of the Jewish Passover. Unlike Victor, however, Telesphorus remained in communion with those communities that did not follow this custom.
The Carmelites venerate Telesphorus as a patron saint of the order since some sources depict him as a hermit living on Mount Carmel.
The town of Saint-Télesphore, in the southwestern part of Canada's Quebec province, is named after him.