  Massive binaries (MBs) play a crucial role in the Universe. Knowing the
distributions of their orbital parameters (OPs) is important for a wide range
of topics, from stellar feedback to binary evolution channels, from the
distribution of supernova types to gravitational wave progenitors, yet, no
direct measurements exist outside the Milky Way. The Tarantula Massive Binary
Monitoring was designed to help fill this gap by obtaining multi-epoch radial
velocity monitoring of 102 MBs in the 30 Dor. In this paper, we analyse 32
VLT/FLAMES observations of 93 O- and 7 B-type binaries. We performed a Fourier
analysis and obtained orbital solutions for 82 systems: 51 single- and 31
double-lined spectroscopic binaries. Overall, the OPs and binary fraction are
remarkably similar across the 30 Dor region and compared to existing Galactic
samples (GSs). This indicates that within these domains environmental effects
are of second order in shaping the properties of MBs. A small difference is
found in the distribution of orbital periods (OrbPs), which is slightly flatter
(in log space) in 30 Dor than in the Galaxy, although this may be compatible
within error estimates and differences in the fitting methodology. Also, OrbPs
in 30 Dor can be as short as 1.1 d; somewhat shorter than seen in GSs. Equal
mass binaries q>0.95 in 30 Dor are all found outside NGC 2070 the very young
and massive cluster at 30 Dor's core. One outstanding exception however is the
fact that earliest spectral types (O2-O7) tend to have shorter OrbPs than
latter (O9.2-O9.7). Our results point to a relative universality of the
incidence rate of MBs and their OPs in the metallicity range from solar
($Z_{\odot}$) to about $0.5Z_{\odot}$. This provides the first direct
constraints on MB properties in massive star-forming galaxies at the Universes
peak of star formation at redshifts z~1 to 2, which are estimated to have
$Z~0.5Z_{\odot}$.
