This paper presents the derivation of the universal (non-spinning) local-in-time conservative dynamics of binary systems at fourth Post-Minkowskian (PM) order, i.e., $ \mathcal{O}(G^4) $. The result is obtained by computing the nonlocal-in-time contribution to the deflection angle and removing it from the total conservative value. The local radial action, center-of-mass momentum, and Hamiltonian are reconstructed, along with the exact logarithmic-dependent parts, valid for generic orbits. The remaining nonlocal terms are incorporated for elliptic-like motion to sixth PM order. The combined Hamiltonian agrees with the state of the art in Post-Newtonian (PN) theory. The derivation involves solving a complex integration problem with two scales—velocity and mass ratio—using differential equations and polylogarithms, complete elliptic integrals, and iterated elliptic integrals. The nonlocal-in-time tail effects are shown to contribute a logarithmic term in the bound dynamics. The results are applied to waveform modeling, providing the most accurate description of gravitationally-bound binaries using scattering data. The local-in-time contribution to the conservative scattering angle is derived by subtracting the nonlocal terms from the total result. The local radial action is obtained via the B2B map, and the center-of-mass momentum and Hamiltonian are reconstructed in isotropic gauge. The results are expanded to 30 orders in the mass ratio and all orders in velocity, with an error beyond 30PN. The nonlocal-in-time effects are shown to contribute a logarithmic term in the bound dynamics, and their inclusion leads to a more accurate description of elliptic-like orbits. The combined Hamiltonian at $ \mathcal{O}(G^4) $ agrees with the state of the art in PN theory. The results are applicable to waveform modeling and provide a framework for incorporating velocity corrections in gravitational wave templates. The paper also discusses the implications of the results for the study of nonlocal-in-time effects in bound orbits and the derivation of a PM version of these effects. The results are supported by references to previous studies and are consistent with the state of the art in gravitational wave astronomy. The work is supported by various grants and acknowledges contributions from multiple researchers.This paper presents the derivation of the universal (non-spinning) local-in-time conservative dynamics of binary systems at fourth Post-Minkowskian (PM) order, i.e., $ \mathcal{O}(G^4) $. The result is obtained by computing the nonlocal-in-time contribution to the deflection angle and removing it from the total conservative value. The local radial action, center-of-mass momentum, and Hamiltonian are reconstructed, along with the exact logarithmic-dependent parts, valid for generic orbits. The remaining nonlocal terms are incorporated for elliptic-like motion to sixth PM order. The combined Hamiltonian agrees with the state of the art in Post-Newtonian (PN) theory. The derivation involves solving a complex integration problem with two scales—velocity and mass ratio—using differential equations and polylogarithms, complete elliptic integrals, and iterated elliptic integrals. The nonlocal-in-time tail effects are shown to contribute a logarithmic term in the bound dynamics. The results are applied to waveform modeling, providing the most accurate description of gravitationally-bound binaries using scattering data. The local-in-time contribution to the conservative scattering angle is derived by subtracting the nonlocal terms from the total result. The local radial action is obtained via the B2B map, and the center-of-mass momentum and Hamiltonian are reconstructed in isotropic gauge. The results are expanded to 30 orders in the mass ratio and all orders in velocity, with an error beyond 30PN. The nonlocal-in-time effects are shown to contribute a logarithmic term in the bound dynamics, and their inclusion leads to a more accurate description of elliptic-like orbits. The combined Hamiltonian at $ \mathcal{O}(G^4) $ agrees with the state of the art in PN theory. The results are applicable to waveform modeling and provide a framework for incorporating velocity corrections in gravitational wave templates. The paper also discusses the implications of the results for the study of nonlocal-in-time effects in bound orbits and the derivation of a PM version of these effects. The results are supported by references to previous studies and are consistent with the state of the art in gravitational wave astronomy. The work is supported by various grants and acknowledges contributions from multiple researchers.