The Writers
The four gospel writers assigned symbols are Matthew, Mark, Luke and John. The books named after them are listed as the first four that compose the New Testament.
The listing of Matthew, Mark, Luke and John represents the chronological sequence of when each gospel was written and finalized. Matthew was penned in 35 A.D. while Mark was written in 42. Luke's gospel was not recorded until 59 A.D. John's book, though mostly composed in 42 A.D., lacked a prologue and epilogue. He did not complete and finalize his text until about 95 A.D.
Origin
The Catholic Church states that early Christian authors, starting in the second century A.D., began to attach a symbol to each gospel writer. They were then followed by artists who began to incorporate them in their work.
"As early as the second century, Christian writers sought in Ezechiel's (Ezekiel's) vision (Ezekiel 1:5) and in Apocalypse (Revelation 4:6 - 10) symbolical representations of the Four Evangelists.
"The system, which finally prevailed in the Latin Church, consisted in symbolizing St. Matthew by a man, St. Mark by a lion, St. Luke by an ox, and St. John by an eagle . . .
"Christian artists followed in the footsteps of the ecclesiastical writers, and made use, in different manners, of the four traditional figures to represent the Evangelists." (1913 Catholic Encyclopedia article entitled Evangelist).
The Catholic system of symbols parallels the sequential imagery of Ezekiel 1:10.
And the likeness of their faces was this: the face of a man (facing front), and the face of a lion, on the right side of the four of them; and the face of a bull on the left side of the four of them; and the face of an eagle toward the rear of the four of them (Ezekiel 1:10, HBFV throughout).
It was sometime after the Catholic theologian Jerome (c. 342 to 420 A.D.) endorsed these symbols and their corresponding evangelist that this system prevailed in the church (History of the Christian Church, chapter 12, The Four Gospels).
Differences
Some early Christian writers differed on which symbol (a man, lion, bull and eagle) should be applied to each gospel author. Irenaeus (c. 122 to c. 202 A.D.), for example, assigned the eagle to Mark and the lion to John (History of the Christian Church). Augustine (354 to 430 A.D.) believed that a lion best represented Matthew and a man best symbolized Mark (ibid.).
Revelation 4 reveals the same faces as the cherubim (see Ezekiel 10) in Ezekiel 1 but in a different order. The order of its imagery used as symbols is a lion, bull (ox), a man and an eagle.
And the first living creature was like a lion, and the second living creature was like a bull, and the third living creature had the face of a man, and the fourth living creature was like a flying eagle (Revelation 4:7).
Several modern commentaries argue that Revelation 4's sequence of images best symbolizes the gospel authors (a lion for Matthew, a bull for Mark, a man for Luke and an eagle for John). They justify this belief by how Christ is represented in each writing.
"Another possible view is that they (Revelation 4:7's images) represent Christ as revealed in the four Gospels: in Matthew, the lion of the tribe of Judah; in Mark, the ox as the servant of Yahweh; in Luke, the incarnate human Jesus; and in John, the eagle as the divine Son of God" (The Bible Knowledge Commentary comments on Revelation 4:7).
". . . there is a definite similarity between the appearance of the four living creatures (in Revelation 4) and the manner by which the four Gospel writers present the earthly ministry of Christ.
"For example: Matthew presents Christ as the Lion of the tribe of Judah. Mark pictures him as the lowly ox. Luke describes the Savior as the perfect man. John paints him to be the lofty eagle" (Wilmington's Complete Guide to Bible Knowledge).
Additional Bible study aids such as Jamieson, Fausset, and Brown's Commentary, A Dictionary of Bible Types, Encyclopedia of Jesus' Life and Time and others support the sequential application of Revelation 4:7's symbols to the gospels.
Other Symbolic Imagery
There are, of course, several other New Testament individuals who have had symbols assigned to them.
"Besides these (the four symbols of the gospels) the other evangelists and the saints carry emblems by which they may be recognized; thus St. Andrew by the (X-shaped) cross, St. Peter by the keys, St. Paul by the sword . . . St. Mary Magdalene by a box or vase . . ." (1911 Encyclopedia Britannica article on Symbol).
The cock, which represents vigilance, is utilized as a symbol for the Apostle Peter (1913 Catholic Encyclopedia article on Birds in Symbolism).
Apostles who were not writers of New Testament books were also assigned symbols. Philip is represented by a basket of loaves and Thomas by a building square. Bartholomew is represented by knives, Jude with a ship, and Matthias with an ax (Catholic Knowledge).