Color centers in diamond are widely explored as qubits in quantum technologies. However, challenges remain in the effective and efficient integration of these diamond-hosted qubits in device heterostructures. Here, nanoscale-thick uniform diamond membranes are synthesized via "smart-cut" and isotopically (¹²C) purified overgrowth. These membranes have tunable thicknesses (demonstrated 50 to 250 nm), are deterministically transferable, have bilaterally atomically flat surfaces (R_q ≤ 0.3 nm), and bulk-diamond-like crystallinity. Color centers are synthesized via both implantation and in situ overgrowth incorporation. Within 110-nm-thick membranes, individual germanium-vacancy (GeV^-) centers exhibit stable photoluminescence at 5.4 K and average optical transition line widths as low as 125 MHz. The room temperature spin coherence of individual nitrogen-vacancy (NV^-) centers shows Ramsey spin dephasing times (T₂^*) and Hahn echo times (T₂) as long as 150 and 400 μs, respectively. This platform enables the straightforward integration of diamond membranes that host coherent color centers into quantum technologies.