The confusing part of this question is that there was no "New Testament" until after everything had been written. And so yes, by the time that the canonical list of New Testament books was compiled (a process that took about 400 years, although the individual books were composed within the first 70) was considered Scripture. Because they were considered Scripture, they were included.
It should be understood that the four Gospels, while only four of many, were the most popular four. Iraneus, in Against the Heresies is insistent that there needed to be four:
the Gospels could not possibly be either more or less in number than they are. Since there are four zones of the world in which we live, and four principal winds, while the Church is spread over all the earth, and the pillar and foundation of the Church is the gospel, and the Spirit of life, it fittingly has four pillars, everywhere breathing out incorruption and revivifying men. From this it is clear that the Word, the artificer of all things, being manifested to men gave us the gospel, fourfold in form but held together by one Spirit.
That said, there were many to choose from. The four we have - Matthew, Mark, Luke, and John, were widely considered the best. Many others (Barnabas, Peter, Judas, Thomas) were either just collected sayings or heretical Gnosticism. Beyond that, others, like Marcion, tried to make their own from scratch. Despite this, these four kept being the most popular, the most profitable, the best for reproof, doctrine, etc...
Bruce Metzger argues that the symbolism may be more of an "after-the-fact" thing, however, saying:
"Among minor [canonical] criteria that the ancients sometimes applied was what may be called 'number-symbolism', of which we have conspicuous examples in Irenaeus and the Muratorian Canon....It is no doubt true that this use of numbers was more often a symbolical interpretation of the facts after the settlement of the different parts of the canon than as a means of determining that settlement." (The Canon Of The New Testament [New York: Oxford University Press, 1997], n. 5 on p. 254)
Over and over again, when seeking to portray an accurate account of how Christians should think and live, however, the stories of these four Gospels kept coming back to the fore as the most important.