The Radak's introduction to Yirmiya explains that the g'mara gives its reasons (the end of M'lachim is churban (destruction), so it matches Yirmiya, and the end of Y'chezkel is nechama (consolation), so it matches Y'sha'ya, yielding the order M'lachim, Yirmiya, Y'chezkel, Y'sha'ya), but the common order, M'lachim, Y'sha'ya, Yirmiya, Y'chezkel, is chronological.
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The gemara has its reasons why it ordered the Tanach that way, and it is discussed there (Bava Basra 14b-15a). However, the custom has become to order it differently in our Tanachs for matters of convenience and chronology.
Neviim Rishonim are ordered chronologically even according to the gemara, as part of their purpose is to record historical fact. Yehoshua, Shoftim, Shmuel, Melachim.
Neviim Acharonim we order chronologically as well, but we do not separate Trei Asar, for fear that small independent nevuos will become lost, and so we place it at the end so as to end with Malachi, the last navi. Yeshayahu, Yirmiyahu, Yechezkel, Trei Asar.
Kesuvim we sort by subject and then chronologically. For convenience, we like to have the "Sifrei Emeth" (א'יוב, 'מ'שלי, 'ת'הלים') together, as well as the five megillos together. First we have the sifrei emeth in chronological order by author: Tehillim, Mishlei, Iyov. [Note that some Tanachs have the order: Tehillim, Iyov, Mishlei. It depends on when you believe Iyov was written. Also, Chazal believe Avraham to be the author of Psalm 89, so that may be why we put Tehillim first.]
Afterwards, we put the five megillos, but instead of ordering them chronologically by author, we order them (again, for convenience's sake,) chronologically by when during the year it is customary to read them publicly (starting with Passover): Shir Hashirim, Ruth, Eicha, Koheles, Esther.
Finally, we have the remaining books of Kesuvim, which we leave in the order that the gemara indicated: Daniel, Ezra/Nechemia, Divrei Hayamim.
(Sources: Abarbanel's introduction to Yeshayahu and an essay on the order and authors of Kesuvim printed in the beginning of Mikraos Gedolos Orim Gedolim Tehillim vol. 1)