The microstructure and crystallographic texture have been investigated in a Cu–45 at.%Ni alloy after heavy rolling and subsequent annealing at different temperatures. Cold-rolling to a von Mises strain of 5.7 produced a sample with an average boundary spacing along the normal direction of ~70 nm and a large fraction of high-angle boundaries (HABs), ~70 %. Annealing of this sample for 1 h at temperatures ≤450 °C causes structural coarsening, during which the fraction of HABs decreases. Annealing at higher temperatures results in pronounced discontinuous recrystallization accompanied by twinning. Large frequencies of twin boundaries contribute to high HAB fractions measured in the as-recrystallized condition. Cube-oriented grains demonstrate a size advantage compared to grains of other orientations, thus creating a strong cube texture in the recrystallized material. Further annealing of the recrystallized microstructure promotes grain growth, which leads to a significant strengthening of the cube texture and to a dramatic loss of HABs. After 1 h of annealing at 1000 °C the fraction of the cube texture reaches 99 % and the HAB fraction is 12 %.