According to Jeremy Crawford, warlocks, at least, were CHA-based in prior editions and the community preferred keeping them that way despite designer preference of making them INT-based in 5e.
@JeremyECrawford Why are Warlock Charisma casters, when their descriptions in the PHB screams Intelligence caster?
(@BringerFiction, 11:34 PM - 16 Dec 2016)
Warlocks used Charisma in previous editions. Playtest feedback wanted that carried forward. (Our preference was to use Intelligence.) #DnD
(@JeremyECrawford, 3:09 PM - 17 Dec 2016)
I don't believe there's any such immediate word-of-designer insight for sorcerers in 5e in particular, though they also were CHA casters in earlier editions.
The charisma based casters became a distinctive feature of 3rd edition, with the Sorcerer. (And the bard, but that's off topic). One of the devs had this to say about the new edition:
TheSage{Skip Williams}: Yes. Wizards use Intelligence, just as they
always have. Sorcerers use Charisma. In the new rules, charisma is
mostly a mental ability, reflecting Strength or will, inner power, and
the like. (Source= RPG Hour: Third Edition D&D Sorcerers, Featuring Skip Williams, designer, Fri. July 20, 2000)
When Warlocks were introduced in The Complete Arcane, they followed the Sorcerer is using will instead of wit for their magical abilities:
Unlike Sorcerers or Wizards, who approach arcane magic through the
medium of spells, a warlock invokes powerful magic through nothing
more than an effort of will. By harnessing his innate magical gift
through fearsome determination and force of will, a warlock can
perform feats of supernatural stealth, beguile the weak minded, or
scour his foes with blasts of eldritch power. page 5
The warlock is described as a new arcane caster:
Born of a supernatural bloodline, a warlock seeks to master the
perilous magic that suffuses his soul.
The decision to use charisma for those two casters was made independently in the editions where they were introduced to the game (3 for Sorcerer and 3.5 for Warlock) but in both cases the designers found that the class "fit" better with the force of will rather than raw intellect to power their magic.
These decision were tied into how the game's chose to change what Charisma represented(see GatesVP answer): in editions 2e and previous, Charisma was about leadership ability, persuasion, and personal magnetism. In subsequent editions, 3 through 5, it is also tied force of personality, force of will.
The other design decision, for the sorcerer in particular, was a choice to provide a non Vancian arcane caster (one who prepared spells in the old way via study of spell books, sort of like charging up a capacitor) or a spontaneous caster, who was not so restricted but who was limited by having available fewer spells. (See also the interview with Skip Williams).
Abelared_DM: I'd like to reiterate my earlier question, from a different angle: What is sorcery all about? You've said that a sorcerer and a wizard look the same when casting a spell... okay, that being said, do they learn their spells in different ways? We know a wizard copies them into a spellbook. How does a sorcerer internalize a new spell? I'm trying to get a philosophical foundation I can build on, here.
TheSage: Sorcerers don't have spell books. How they internalize spells
is largely unrevealed. It is assumed that sorcerers learn new spells
through research and meditation, much as wizards do. Sorcerers do not
prepare spells ahead of time. They simply use what they know until
they're tapped out magically for the day.
Further detail on this can be found at Q&A here, and here.