Morphologization

Morphologization is the process by which linguistic structures which previously belonged to a different domain of grammar become part of the morphological system of a language.

In morphologization "[P]honological processes and syntactic structures [...] become properly an aspect of morphological, rather than phonological or syntactic, organization" (Fox 1995: 102). As pointed out in the previous quote the two sources morphologizied structures can originate from are the phonological and the syntactic domain of grammar. Those two types of morphologization have also been labeled dephonologization and desyntactization respectively (Joseph 2003: 473).

Examples
Morphologization from phonology:

An example for morphologization of phonological rules is the German plural-ablaut (see e.g. Lass 1990: 98f). The Old High German productive system of vowel harmony changed the underlying back vowels of noun-stems to their front counterparts in a class of nouns taking the plural-suffix -i. Those nouns kept the plural-umlaut after vowel harmony was lost. Morphologization set in when via analogy the umlaut-formation in plural forms was extended to classes of nouns which never had the '-i' plural-suffix. Thus the phonological rule which changed stem-vowels from back to front in the context of the affixal front-vowel i, changed to a morphological rule which led to umlaut-formation in plural-contexts. This strategy has been described as an instance of exaptation by Lass (1990)

Morphologization from syntax:

Morphologization from syntactic structures is one of the core issues dealt with in grammaticalization theory. All instances where a previously independent word turns into a bound morphological item exemplify the process of morphologization. One example is the French adverb-forming suffix -ment, which has its origin in the Latin noun stem ment- 'mind' (Joseph 2003:472f.). This is a clear instance of the path from independent noun (syntactic item) to dependent affix (morphological item).