  We derive the classical gravitational radiation from an aligned spin binary
black hole on \textit{closed} orbits, using a dictionary built from the 5-point
QFT scattering amplitude of two massive particles exchanging and emitting a
graviton. We show explicitly the agreement of the transverse-traceless
components of the radiative linear metric perturbations -- and the
corresponding gravitational wave energy flux -- at future null infinity,
derived from the scattering amplitude and those derived utilizing an effective
worldline action in conjunction with multipolar post-Minkowskian matching. At
the tree-level, this result holds at leading orders in the black holes'
velocities and up to quadratic order in their spins. At sub-leading order in
black holes' velocities, we demonstrate a matching of the radiation field for
quasi-circular orbits in the no-spin limit. At the level of the radiation
field, and to leading order in the velocities, there exists a one-to-one
correspondence between the binary black hole mass and current quadrupole
moments, and the scalar and linear-in-spin scattering amplitudes, respectively.
Therefore, we show explicitly that waveforms, needed to detect gravitational
waves from \textit{inspiraling} binary black holes, can be derived
consistently, to the orders considered, from the classical limit of quantum
\textit{scattering} amplitudes.
