How long has the subjunctive existed in English?

Short Answer

The subjunctive mood has always existed in English. It in the Old English of Beowulf and in the Middle English of Chaucer and the English of Shakespeare.

Expansion

The question suggests a misconception that the subjunctive mood is something that was acquired at some stage in the development of English. In fact the subjunctive mood is a feature of Indo-European languages, including the Germanic ancestor of Old English, even if its usage changed during the development of the language into Modern English, where it is much less used than previously.

Web references to the subjunctive in different ancestors of English

General coverage of subjunctive in different languages

Proto-Indo-European

Old English (aka Anglo-Saxon) and Middle English etc.

Quotations

BEOWULF:

Here swice and scolde illustrate the subjunctive mood (N.J.Engberg).

CHAUCER:

It is ful lasse harm to lete hym pace, Than he shende alle the servantz in the place.

Here shende is subjunctive, used after than.

SHAKESPEARE

Be thou a spirit of health or goblin damn'd, Bring with thee airs from heaven or blasts from hell, Be thy intents wicked or charitable, Thou comest us such a questionable shape that I will speak to thee ...

In this extract from Hamlet the italicized words are in the subjunctive mood.