Curiously, Old English unc is actually not related to German uns, at least, not after the Germanic language family had already formed. Old English at some point underwent a sound change[1] where the -n- sound disappeared before fricatives (sounds like s, f, v, z, sh, etc...). So "us" comes from an older common form "uns", which German inherited basically unchanged. This sound change also explains other correspondences between English and German where the n is missing, like mouth-Mund, tooth-Zahn, other-ander, goose-Gans or five-fünf.
1: https://en.wikipedia.org/wiki/Ingvaeonic_nasal_spirant_law