  We prove the existence of an $m$-cluster tilting object in a generalized
$m$-cluster category which is $(m+1)$-Calabi-Yau and Hom-finite, arising from
an $(m+2)$-Calabi-Yau dg algebra. This is a generalization of the result for
the ${m = 1}$ case in Amiot's Ph.~D.~thesis. Our results apply in particular to
higher cluster categories associated to suitable finite-dimensional algebras of
finite global dimension, and higher cluster categories associated to Ginzburg
dg categories coming from suitable graded quivers with superpotential.
