Small print: This is language specific about English, but tangential to Germanic to a certain degree that is likely out of ELU's scope. .
As a follow-up to this Q and several ones like it about the difference between school grammar and linguists categorisation, I wondered about the origin of "will", just because ...
Wikipedia notes about the Proto-Indo-European subjunctive (bold emphasis mine):
The subjunctive mood was used to describe completely hypothetical events, along the lines of "suppose that I oversleep...". It was also sometimes used for future events (which are by definition hypothetical rather than actual) for this reason.
The subjunctive was formed by adding the thematic vowel to the stem, along with primary endings, with the stem in the e-grade. The subjunctive of athematic verbs was thus thematic, and morphologically indistinguishable from a thematic indicative. For verbs that were already thematic, a second thematic vowel was added after the first, creating a long thematic vowel.
Wiktionary derives will thus:
[…] from Proto-Germanic *wiljaną (“to desire, wish”), from Proto-Indo-European *welh₁- (“to choose, wish”). […] The verb is not always distinguishable from Etymology 3, below.
[…] from Old English willian (“to will”), from Proto-Germanic *wiljōną (“to will”), from Proto-Indo-European *welh₁- (“to choose, wish”).
Indeed, the firstly mentioned PGem root is mainly subjunctive:
From Proto-Indo-European *wélyoyt, optative of *wélyeti, from *welh₁- (“to choose, to want”).
Inflection: Only subjunctive forms exist in the present tense. The past tense is declined as a suffixless weak verb.
For perspective, note:
The optative has been consolidated in Germanic. It is derelict in nearly all branches of IE. 
They derive *wiljona (i.e. will 3) from *wiljana, whereby the underlying PIE optative already shows o in the thematic vowel. This level of indirection (*o > *a > *o) might be formally necessary, or just a simplified account, I'm not sure.
Another ablaut relates *waljana "to choose", which they explain redundantly as "From *wiljaną + *-janą.".
This poses several questions, before we can get to the English word.
What does the vowel alternation in the ablaut mean?
Was "will" used to form future semantics in common Germanic?
The Old English account should at best confirm the reconstruction, insofar German "willst du wohl", e.g. does largely agree. I have not considered the negated form so far.
1: Wolfram Euler, Die Rolle von Etymologie und Grammatik in Sprachentwicklung und Sprachverwandtschaft, 2012