  The non-thermal emission from the kiloparsec-scale jet of Centaurus A
exhibits two notable features, bright diffuse emission and many compact knots,
which have been intensively studied in X-ray and radio observations. H.E.S.S.
recently reported that the very-high-energy gamma-ray emission from this object
is extended along the jet direction beyond a kiloparsec from the core. Here, we
combine these observations to constrain the physical conditions of the kpc-jet
and study the origin of the non-thermal emission. We show that the diffuse jet
is weakly magnetized ($\eta_B\sim10^{-2}$) and energetically dominated by
thermal particles. We also show that knots are the sites of both amplified
magnetic field and particle (re-)acceleration. To keep sufficient energy in
thermal particles, the magnetic and non-thermal particle energy in the knot
regions are tightly constrained. The most plausible condition is an energy
equipartition between them, $\eta_B\sim\eta_e\sim0.1$. Such weak magnetic
energy implies that particles in the knots are in the slow cooling regime. We
suggest that the entire kpc-scale diffuse emission could be powered by
particles that are accelerated at and escaped from knots.
