When was the writing of the New Testament completed?  

• I will provide my answer now: by the end of the Apostles generation, -- before about 70 A.D.

Read the balance of this page to see why I answer as I do.

I can offer several things that should be considered regarding this question.

In order for something to be considered to be authoritative and inspired Scripture, it must have proceeded from the apostles chosen by Jesus or by on of the apostles' chosen assistants.

Consider the pattern of the offices.

There were four offices that operated for the Old Covenant: prophets, priests, judges and kings.  

• They were directly called by God.

• The prophets could use assistants and they often did.

• They were sometimes referred to as "sons" of the prophets.

• Their ministries continued for as long as the prophets they were connected to lived.

• The sons of the prophets could not create more sons of the prophets.

There are four offices that have operated for the New Covenant: apostles, prophets, evangelists, and pastor-teachers.

• They were directly called by God (Jesus Christ).

• The apostles could use assistants and they often did.

• The apostles often referred to them as their "sons".

• Their ministries continued for as long as the apostles that they were connected to lived.

• The sons of the apostles could not create more sons of the apostles.

Consider the restriction to one generation.

Jesus Promised the generation in which He lived that He would be sending them to them specifically. I t would be that generation that would have these messengers from God (that is Jesus Christ).

Matt. 23:36-38

[34] Wherefore, behold, I send unto you prophets, and wise men, and scribes: and some of them ye shall kill and crucify; and some of them shall ye scourge in your synagogues, and persecute them from city to city:
[35] That upon you may come all the righteous blood shed upon the earth, from the blood of righteous Abel unto the blood of Zacharias son of Barachias, whom ye slew between the temple and the altar.
[36] Verily I say unto you, All these things shall come upon this generation.
[37] O Jerusalem, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not!
[38] Behold, your house is left unto you desolate.

Luke 11:42-54

[42] But woe unto you, Pharisees! for ye tithe mint and rue and all manner of herbs, and pass over judgment and the love of God: these ought ye to have done, and not to leave the other undone.
[43] Woe unto you, Pharisees! for ye love the uppermost seats in the synagogues, and greetings in the markets.
[44] Woe unto you, scribes and Pharisees, hypocrites! for ye are as graves which appear not, and the men that walk over them are not aware of them.
[45] Then answered one of the lawyers, and said unto him, Master, thus saying thou reproachest us also.
[46] And he said, Woe unto you also, ye lawyers! for ye lade men with burdens grievous to be borne, and ye yourselves touch not the burdens with one of your fingers.
[47] Woe unto you! for ye build the sepulchres of the prophets, and your fathers killed them.
[48] Truly ye bear witness that ye allow the deeds of your fathers: for they indeed killed them, and ye build their sepulchres.
[49] Therefore also said the wisdom of God, I will send them prophets and apostles, and some of them they shall slay and persecute:
[50] That the blood of all the prophets, which was shed from the foundation of the world, may be required of this generation;
[51] From the blood of Abel unto the blood of Zacharias, which perished between the altar and the temple: verily I say unto you, It shall be required of this generation.
[52] Woe unto you, lawyers! for ye have taken away the key of knowledge: ye entered not in yourselves, and them that were entering in ye hindered.
[53] And as he said these things unto them, the scribes and the Pharisees began to urge him vehemently, and to provoke him to speak of many things:
[54] Laying wait for him, and seeking to catch something out of his mouth, that they might accuse him.

Consider New Testament Internal Evidence

It is extremely unwise to rely upon history when trying to come to ultimate truth, since history is full of deception.  W hat is referred to as "higher criticism" always wants to date the writing of the Scriptures to later than what they actually were, because they want to diminish the power of God's Word and make an easy way for them to try to explain away things.

When internal evidence can be found, it should be cited and relied upon with confidence.

Evidence: the letter to the Hebrews

Some translations will ascribe the author of the letter to the Hebrews as Paul. However, there is no direct manuscript evidence for this. There is internal evidence within the letter that points towards Paul. that is not the point that I'm making here.  I don't think it is incredibly important to be able to assign the authorship to an individual.   The author was no doubt a highly educated Hebrew believer in Jesus Christ, and the contents certainly contains apostolic authority.

See "not of this building" below.

Heb. 9:1-18

[1] Then verily the first covenant had also ordinances of divine service, and a worldly sanctuary.
[2] For there was a tabernacle made; the first, wherein was the candlestick, and the table, and the shewbread; which is called the sanctuary.
[3] And after the second veil, the tabernacle which is called the Holiest of all;
[4] Which had the golden censer, and the ark of the covenant overlaid round about with gold, wherein was the golden pot that had manna, and Aaron's rod that budded, and the tables of the covenant;
[5] And over it the cherubims of glory shadowing the mercyseat; of which we cannot now speak particularly.
[6] Now when these things were thus ordained, the priests went always into the first tabernacle, accomplishing the service of God.
[7] But into the second went the high priest alone once every year, not without blood, which he offered for himself, and for the errors of the people:
[8] The Holy Ghost this signifying, that the way into the holiest of all was not yet made manifest, while as the first tabernacle was yet standing:
[9] Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience;
[10] Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation.
[11] But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building;
[12] Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us.
[13] For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh:
[14] How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
[15] And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
[16] For where a testament is, there must also of necessity be the death of the testator.
[17] For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.
[18] Whereupon neither the first testament was dedicated without blood.

The author of Hebrews has been making the point of how Jesus was better or Superior to everything. Better than Moses, better than angels, better than the temple or the tabernacle. and the highlighted verse there is a reference to a current building. The Temple was destroyed about 70 AD.  

The writer did not say not of that building or not of the former building. H e used language to point to a building that was still standing. Hebrews, like the rest of the New Testament was completed before 70 AD.