  Until recently, the strong interstellar scattering observed towards the
Galactic center (GC) black hole, Sgr A*, was thought to come from dense gas
within the GC region. The pulse broadening towards the transient magnetar SGR
J1745-2900 near Sgr A* has shown that the source of the scattering is instead
located much closer to Earth, possibly in a nearby spiral arm. We show that a
single HII region along the line of sight, 1.5-4.8 kpc away from Earth with
density $n_e$ of a few 100 cm$^{-3}$ and radius R = 1.8-3.2 pc can explain the
observed angular broadening of Sgr A*. Clouds closer to the GC overproduce the
observed DM, providing an independent location constraint that agrees with that
from the magnetar pulse broadening. Our model predicts that sources within 10
pc should show the same scattering origin as the magnetar and Sgr A*, while the
nearest known pulsars with separations > 20 pc should not. The radio spectrum
of Sgr A* should show a cutoff from free-free absorption at 0.2-1 GHz. For a
magnetic field strength $B = 15-70 \mu$G, the HII region could produce the
rotation measure of the magnetar, the largest of any known pulsar, without
requiring the gas near Sgr A* to be strongly magnetised.
