It's already noted in another question that to be was used to form the perfect aspect, being replaced by to have in this role, but gradually so that to be was used of verbs of motion, to indicate the state arrived at (to have coming into this axillary role in Old English, and established into it in early Middle English, but to be still not entirely replaced when it comes to verbs of motion by early Modern). It persists in poetic use, for which it being relatively well-known from the KJV will likely keep it alive for some time, and in some dialects (often in variants such as "I do be doing that every day" which isn't even a verb of motion, though likely of foreign influence), but is pretty much on the threshold between archaic and obsolete as far as standard English goes.
When it came in is more controversial. While it's known to be the earliest perfect form, just how early is debated:
It might reasonably be expected that the grammaticalization of Germanic periphrastic perfects followed lines similar to those of the corresponding Romance process, given the semantic similarity of the two groups in regard to their past-participle morphology and the lexical verbs from which the auxiliaries are derived; however, it will be seen that the evidence for the Germanic languages is sparser in some respects and allows for greater differences in interpretation. The semantic pathways by which the grammaticalization of these constructions took
place are generally uncontroversial, despite some variation as to which of the senses of the polysemic verbs involved contributed most to their becoming auxiliaries (for discussion see de Acosta 2006, 1–17). However, greater controversy exists regarding the points at which different stages in this process were reached. Brinton considers the grammaticalization of periphrastic perfects to have been already in progress at the Common Germanic period; she argues that alternative explanations require ‘independent parallel variations of an unlikely extent’ (1988, 107). In contrast, others have observed (e.g. Harbert 2007, 301–2) that the use of the preterite in Gothic and Old High German as the sole translation equivalent for the Latin imperfect, perfect, and pluperfect, as well as the high degree of variation found among the Germanic languages both in the selection of auxiliaries by individual verbs and in the verbs that are used as auxiliaries of the perfect (with some languages extending beyond the basic verbs meaning ‘have’ and ‘be’ to make use of verbs meaning ‘own’ or ‘become’), would seem to suggest a certain degree of independent innovation in the individual Germanic languages. It will be seen in Section 1.3.3 below that some studies on Old English conclude that these periphrastic constructions were still at an extremely primitive stage in the earliest recorded texts; in this way, they too advocate a late date for much of the development of these constructions. Mention might also be made of the suggestion that the Germanic perfect periphrases have their origin in calques of similar Latin constructions; Drinka (2003; 2007), a recent proponent of this view, asserts that given the existence of these constructions in Latin, as well as the exposure of the Germanic-speaking peoples to Latin and their physical proximity to Romance speakers, areal diffusion is a more parsimonious explanation than
independent innovation. It should be noted that such a view does not preclude the possibility of different processes of borrowing in different Germanic languages, and is therefore not necessarily incompatible with the variation described by Harbert (2007). Nevertheless, there is little positive evidence to connect the Latin constructions with those found in the Germanic languages, or for the high degree of influence which Latin texts would presumably need to exert upon the vernacular language (see de Acosta 2006, 17–19). As discussed above, the evidence for the earliest stages of the Germanic languages is seldom sufficient to confirm or disprove specific hypotheses, but given the absence of any conclusive evidence against the independent development of perfects, not only within Germanic as a separate group but separately within individual languages, together with the cross-linguistic frequency of developments of this sort (e.g. Bybee et al. 1994, 68–9), it is assumed here that some degree of independent innovation in the history of Germanic perfects is a simpler explanation than one involving borrowing. The comparison of translated Old English texts with their Latin originals in Section 220.127.116.11 below will provide further support for this position.
The thesis I quote from can be consulted for more.
So, it's possible that it originated before English was English, but there's also considerable evidence to suggest it originated during the Old English period, separate (though perhaps influenced by) the same happening to other Germanic languages.
Judging just which of those experts is right is way beyond my reach.