  We propose a new analytical expression for the Transverse Momentum Dependent
(TMD, or unintegrated) gluon density in the proton. Essential phenomenological
parameters are extracted from the LHC data on inclusive hadron production in
$pp$ collisions at low transverse momenta, $p_T \sim 1$~GeV. The latter are
described in the framework of modified soft quark-gluon string model, where
gluonic state and non-zero transverse momentum of partons inside the proton are
taken into account. To determine the parameters important at moderate and large
$x$ we used measurements of inclusive $b$-jet and Higgs boson production at the
LHC as well as latest HERA data on proton structure functions $F_2^c(x, Q^2)$
and $F_2^b(x, Q^2)$ and reduced cross sections $\sigma_{\rm red}^{c}(x,Q^2)$
and $\sigma_{\rm red}^{b}(x,Q^2)$. The Catani-Ciafaloni-Fiorani-Marchesini
evolution equation is applied to extend the initial gluon distribution into the
whole kinematical region. We have achieved simultaneous description of all
considered processes with $\chi^2/d.o.f. = 2.2$, thus moving forward to the
global fit of TMD gluon density from collider data. The obtained TMD gluon
distribution in a proton is available for public usage and implemented into the
TMDlib package and Monte-Carlo event generator PEGASUS.
