Traditionally, the four Gospel writers have been represented by the following symbols (as indicated in the question):
St. Matthew, a divine man;
St. Mark, a winged lion;
St. Luke, a winged ox; and
St. John, a rising eagle.
These symbols are taken first from the Prophet Ezekiel (1:1-21):
"In the 30th year, on the fifth day of the fourth month, while I was among the exiles by the river Chebar, the heavens opened, and I saw divine visions…. As I looked, a stormwind came from the north, a huge cloud with flashing fire, from the midst of which something gleamed like electrum. Within it were figures resembling four living creatures that looked like this: their form was human, but each had four faces and four wings, and their legs went straight down; the soles of their feet were round. They sparkled with a gleam like burnished bronze. Their faces were like this: each of the four had a face of a man, but on the right side was the face of a lion, and on the left side the face of an ox, and finally each had the face of an eagle…."