I will be answering from Islamic sources.

The Quran was not revealed chapter by chapter but by groupings of verses. For example the first revelation was only the first 5 verses of Surah Alaq, A surah that has 19 verses total. Read Chronologically as it was revealed, would mean chopping up chapters here and there and while meanings of specific passages might remain intact they would lose their greater context in the placement within the specific chapters that those passages are a part of. That said when one studies Tafsir (Quranic exegis) the time, place, and circumstance of that passage being revealed is also studied, provided such specific information is known.

In this matter there is consensus amongst Islamic Scholars regarding the ordering and placement of verses were established before the death of the Prophet and there are Hadeeth which narrate incidents where the Prophet would mention that such and such verses are part of such and such Surah. These examples range from statements by various senior companions to the Prophet himself. As just one example, quoting the translation of the relevant part out of a Hadith from Saheeh Muslim , Book of Inheritance, where Umar bin Al Khattab was relating the response of the Prophet to a question about the inheritance of the one who dies without any living direct descendants

Umar, does the ayat-us-sayf, at the end of Sura al-Nisa' does not suffice you?

There are other narrations more directly related to the ordering of verses but I'm more comfortable quoting out of Saheeh Muslim for a quick example. So regarding the actual ordering of the verses within their chapters, there isn't any disagreement amongst Islamic Scholars, at least amongst the Sunni schools.

Now onto the actual ordering of the Surahs this is actually down to two scholarly opinions. Either the order that is preserved in the Manuscript of Uthman was given by the Prophet or it was set down by the deliberation and consensus of the Senior Companions of the Prophet. Even amongst those of the latter opinion there's a lot of leeway that the preferred order of most of the chapters was known prior to the death of the Prophet. The majority opinion seems to be that while a lot of the ordering of Surahs were known before the death of the Prophet, some were still left up to the deliberation of the companions.

Amongst the companions though, there wasn't really a full on consensus regarding that ordering. There were in fact other Manuscripts before the Manuscript of Uthman was standardized that had different orderings like the Manuscript of Ubayy bin Ka'ab which started with Surah Al Baqara then Surah An Nisa' and then Surah Al Imran which is different from the Uthmani Manuscript which places Imran before Nisa' along with other major changes. Ultimately though the order that is in the Manuscript of Uthman is the one that survived to today and I am not aware of any more recent attempts to change that order.

So to sun up the answer, according to Islamic sources, the order of chapters was mostly decided and taught by the Prophet himself and what parts were uncertain were placed by the companions through Ijtihaad