Academic scholars generally agree that the book was finalized near the end the reign of Antiochus Epiphanes, i.e. 165 BCE when the Temple was rededicated after the Maccabean revolt. It was in this period when ch. 8-12 in Hebrew were written. Many scholars also believe that the chapters in Aramaic are older, particularly the stories about Daniel, which may have took shape in the fourth and third centuries BCE. See the many critical commentaries on Daniel for a lengthy discussion, such as the Hermeneia volume by John J. Collins, the ICC volume by Montgomery, or the Anchor Bible (Vol. 23) commentary by Louis Hartman and Alexander DiLella. Rainer Albertz in Daniel: Composition and Reception (Brill, 2001) discusses the book of Daniel as a rolling corpus. The oldest material is ch. 4-6 which exists in a rather different recension in the OG, which Albertz dates to c. 250 BCE reflecting the social situation in that period. Then an Aramaic version was composed c. 200 BCE in the reign of Antiochus III which turned the work into an apocalypse with the addition of ch. 2-3 and 7. This created a symmetric chiasm with the central story of ch. 4-5 flanked with stories of resistance to idolatry with divine help (ch. 3 and 6), and then the two visions of the four kingdoms (c. 2 and 7). Then possibly the “little horn” material in ch. 7 was added when Antiochus’ persecution started and the book was completed in c. 165 BCE with the addition of the Hebrew material.
Collins in his Hermeneia commentary gives a detailed survey of the linguistic data on the Aramaic on pp. 13-18. There can be a good deal of synchronic variation in features and so it can be tricky to develop a relative chronology of linguistic changes separated by only a few hundred years. We have a few Imperial Aramaic texts from the sixth and fifth centuries BCE (such as the Persepolis fortification tablets), the Elephantine, Hermopolis, and Padua papyri from the fifth century BCE, the Samaria papyri from the fourth century BCE, the Aramaic portions of Ezra which used to be dated to the fifth century but now are commonly dated a century later, the Enochic Book of Watchers, Book of Luminaries, and the Book of Giants from the third century BCE, and the Genesis Apocryphon and other Qumran Aramaic texts from the second and first centuries BCE. Collins concludes that “the Aramaic of Daniel appears to be later than that of the Samaria papyri, while it does not attest many of the developments found in the Dead Sea Scrolls. The balance of probability, then, favors a date in the early Hellenistic period for the Aramaic portions of Daniel, although a precise dating on linguistic grounds is not possible” (p. 17).
There are other features in the text which show that the Aramaic is not from the sixth century BCE. The Aramaic portions of Daniel are very dense with Persian loanwords (some 17 in all), which is far higher than what is found in the Aramaic translation of the Behistun inscription (namely, none) and the Elephantine letters (see Montgomery’s ICC volume, p. 21). Aren Wilson-Wright (VT, 2015) notes that in the case of Hebrew, Persian loanwords (which also occur in the Hebrew sections of Daniel) do not begin to appear until after the middle of the fifth century BCE. Interestingly, the loanwords are most frequent in the stories set in the Neo-Babylonian period, with even Nebuchadnezzar using them in his first-person account (4:6); Nebuchadnezzar is also depicted unintentionally as ignorant of his own language Akkadian (making a blunder in 4:8).
The late vocabulary in Daniel 3 is most noticeable because it is studded with six different Persian administrative titles (including satraps) which would have surely not been used in Nebuchadnezzar’s government. The narrative also includes three Greek words of musical instruments, one of which (סימפוניה, cf. συμφωνία) is not known to have existed until Hellenistic times. There is otherwise no contemporary evidence of those words and instruments being used in Babylon during the Neo-Babylonian period. The less strained explanation is that the words are in the story because the story itself was written in Hellenistic times when Greek culture was more widely diffused in the Levant. Finally, the Greek vocabulary may not be limited to the musical instruments but also the word for the “herald” (כרוז, cf. κῆρυξ) in 3:4 has strong claims as having a Greek derivation as well. Generally, Greek loanwords appear very late in Hebrew and Aramaic. Ben Sira (early second century BCE) has only one example and it is uncertain on account of preservation of the manuscript. The only Greek loanwords at Qumran were found in the Copper Scroll, probably the latest composition in the caves (dating to after the Jewish revolt of 70 CE), with no examples in the Aramaic and sectarian Hebrew compositions, with loanwords becoming much more common in Mishnaic Hebrew.
Also the paleographical dating of the Qumran manuscripts is not accurately presented here. Eugene Ulrich dates the oldest MS (4QDanᶜ) to “late 2nd or early 1st c. BCE” on paleographical grounds (Book of Daniel: Composition and Reception, Vol. 2, p. 574). Collins quotes the assessment by Frank Moore Cross that it dates to “the late second century … no more than about a half century younger than the autograph” (p. 2). There are also other MSS at Qumran that date later in the first century BCE, as well as in the first century CE (such as the two first cave MSS and pap6QDan). The Dead Sea Scrolls may also contain various sources utilized or related to those utilized by the author(s) of Daniel, such as the Book of Giants, the prayer in 4QDanᵉ, 4Q242 (Prayer of Nabonidus), and 4Q248 (Acts of a Greek King). So the oldest MS dates to c. 100 BCE, about 50 or 60 years after the autograph, keeping in mind that paleography is inexact. This is comparable to some of the oldest NT manuscripts.

At the end of the Greek book of Daniel there are three further stories involving Daniel: the story of Susanna (ch. 13 in NRSV), the story of Bel (14: 1–22), and the story of the Dragon (14: 23–42). As mentioned above, Tal Ilan (1999) argues that the books of Judith and Esther and the story of Susanna were all written as propaganda to support the rule of Queen Salome Alexandra (76–67 bce). Clanton (2003) further reWnes this idea by suggesting that the attitude to perjury in Susanna reXects the position of the Pharisees, who were the dominant party during Salome Alexandra’s reign.