  We compute the unpolarized quark and gluon transverse-momentum dependent
fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order
(N$^3$LO) in perturbative QCD. The calculation is based on a relation between
the TMDFF and the limit of the semi-inclusive deep inelastic scattering cross
section where all final-state radiation becomes collinear to the detected
hadron. The required cross section is obtained by analytically continuing our
recent computation of the Drell-Yan and Higgs boson production cross section at
N$^3$LO expanded around the limit of all final-state radiation becoming
collinear to one of the initial states. Our results agree with a recent
independent calculation by Luo et al.
