Question:

Is it a mitzvah for a divorced couple to remarry one another?

Answer:

Yes. The Jerusalem Talmud1 see this in Isaiah 58:7, where the prophet exhorts the Jew not to "hide from your flesh," i.e. to look out for our relatives. Rabbi Yaakov says in the name of Rabbi Eleazar that this applies even to one's ex-wife.

While the Talmud does not explicitly say that the way one takes care of his ex-wife is by remarrying her, many later halachic authorities understand the Talmud to be saying that it is a mitzvah to remarry one's ex-wife.2

It is important to note that, nevertheless, the Torah explicitly prohibits remarrying once a woman has been married to another man in the interim.3 It is also forbidden for a Kohen to remarry a divorcee, including his own ex-wife.4