Development of reaction zones at the core Mg(Cu) – boron (B) and barrier (Ti) – sheath (Cu) interfaces of an internal magnesium diffusion (IMD) manufactured MgB2 composite wire has been studied at varying temperatures of 560–665 °C for 30 min and varying time periods of 30–180 min at 560 °C. MgB2 has predominantly formed at the Mg(Cu) – B interface with little solubility of Cu of 1–3 at%. A second phase enriched with Cu, Mg2Cu, has also formed at random locations within the MgB2 phase matrix, indicating the advantage of doping Cu in the Mg rod. However, a layer of another B-rich phase, MgB4, has also formed at a higher temperature of 665 °C with negligible solubility of Cu at the MgB2 – B interface. At the Ti – Cu interface, the formation of CuTi2, CuTi, Cu4Ti and Cu4Ti3 intermetallic phases took place. However, the Cu4Ti and Cu4Ti3 phases develop after annealing the wire at a relatively higher temperature of 620 °C and at 560 °C with progress in annealing time. Critical current density (Jc) decreases with annealing time; however, the sensitivity of Jc towards annealing time is low. Critical current density is found to be strongly dependent on the annealing temperature of the composite wires for the formation of the MgB2 superconductor phase. A maximum critical current density of ∼ 2.5 × 104 A/cm2 at 5 T and 4.2 K is attained for the Cu-doped MgB2 composite wire when annealed at 665 °C for 30 min. A maximum shift of only 0.5 K is measured for MgB2 when formed at the highest annealed temperature compared to the lowest one in this study.