  The Fermi bubbles are two large structures in the gamma-ray sky extending to
$55^\circ$ above and below the Galactic center. We analyze 50 months of Fermi
Large Area Telescope data between 100 MeV and 500 GeV above $10^\circ$ in
Galactic latitude to derive the spectrum and morphology of the Fermi bubbles.
We thoroughly explore the systematic uncertainties that arise when modeling the
Galactic diffuse emission through two separate approaches. The gamma-ray
spectrum is well described by either a log parabola or a power law with an
exponential cutoff. We exclude a simple power law with more than 7$\sigma$
significance. The power law with an exponential cutoff has an index of $1.9 \pm
0.2$ and a cutoff energy of $110\pm 50$ GeV. We find that the gamma-ray
luminosity of the bubbles is $4.4^{+2.4}_{-0.9} \times 10^{37}$ erg s$^{-1}$.
We confirm a significant enhancement of gamma-ray emission in the south-eastern
part of the bubbles, but we do not find significant evidence for a jet. No
significant variation of the spectrum across the bubbles is detected. The width
of the boundary of the bubbles is estimated to be $3.4^{+3.7}_{-2.6}$ deg. Both
inverse Compton (IC) models and hadronic models including IC emission from
secondary leptons fit the gamma-ray data well. In the IC scenario, the
synchrotron emission from the same population of electrons can also explain the
WMAP and Planck microwave haze with a magnetic field between 5 and 20 $\mu$G.
