  The non-linear dynamics of General Relativity leave their imprint on remnants
of black hole mergers in the form of a recoil ``kick''. The kick has profound
astrophysical implications across the black hole mass range from stellar to
super-massive. However, a robust measurement of the kick for generic binaries
from gravitational-wave observations has proved so far to be extremely
challenging. In this \emph{letter}, we demonstrate the prospects of measuring
black hole kicks through a multiband gravitational-wave network consisting of
space mission LISA, the current earth-based detector network and a
third-generation detector. For two distinct cases of remnant black hole kick
(68 km/s, 1006 km/s) emerging from near identical pre-merger configuration of
GW190521 -- the first confirmed intermediate-mass black hole -- we find that
the multiband network will recover with 90\% credible level the projection of
the kick vector relative to the orbital plane within tens of km/s accuracy.
Such precise measurement of the kick offer a new set of multi-messenger
follow-ups and unprecedented tests of astrophysical formation channels.
