The premonition, upon first meeting someone, that the two of you will inevitably fall in love.
The premonition, upon first meeting someone, that the two of you will inevitably fall in love — a sense that love is coming, though it has not yet arrived.
Crucially NOT love at first sight — that is a separate, common word, hitomebore (一目惚れ), denoting instant present-tense infatuation. Koi no yokan is future-oriented: no love or even attraction need exist yet; what is present is the forecast that it will come. Quiet by definition, unlike the giddy thrill of kilig or the lightning-jolt of coup de foudre, and distinct from the already-active obsession of limerence.
koi “love” + no (genitive) + yokan “premonition” = “premonition of love.”
A transparent compositional phrase: 恋 koi “love,” の no, 予感 yokan “premonition” (予 “beforehand” + 感 “feeling”).
A real, natural Japanese expression in ordinary use. Some English writing layers a Buddhist “karmic connection across lifetimes” reading onto it — an embellishment by popularizers, not the plain sense.
A genuine Japanese phrase, but very frequently mis-glossed in English as “love at first sight” — that is wrong (Japanese has hitomebore for that). The “mystical / karmic soulmate” framing is added by listicles; the core meaning (a premonition of future love) is sound.