Wake evolution of an oscillating foil with combined heaving and pitching motion is evaluated numerically for a range of phase offsets (
$\phi$), chord-based Strouhal numbers (
$St_c$) and Reynolds numbers (
$Re$). The increase in
$\phi$ from
$90^\circ$ to
$180^\circ$ at a given
$St_c$ and
$Re$ coincides with a transition of pitch- to heave-dominated kinematics that further reveals novel transitions in wake topology characterized by bifurcated vortex streets. At
$Re= 1000$, each of the dual streets constitutes a dipole-like paired configuration of counter-rotating coherent structures that resemble qualitatively the formation of
$2P$ mode. A new mathematical relation between the relative circulation of coherent dipole-like paired structures and kinematic parameters is proposed, including heave-based (
$St_h$), pitch-based (
$St_{\theta }$) and combined motion (
$St_A$) Strouhal numbers, as well as
$\phi$. This model can predict accurately the wake transition towards
$2P$ mode characterized by a bifurcation, at low
$Re= 1000$. At
$Re= 4000$, however, the relationship was inaccurate in predicting the wake transition. A shear splitting process is observed at
$Re= 4000$, which leads to the formation of reverse Bénard–von Kármán mode in conjunction with
$2P$ mode. Increasing
$\phi$ further depicts a consistent prolongation of the splitting process, which coincides with a unique transition in terms of absence and reappearance of bifurcated dipole-like pairs at
$\phi = 120^\circ$ and
$180^\circ$, respectively. Changes in the spatial arrangement of
$2P$ pairs observed consistently for oscillating foils with the combined motion constitute a novel wake transition that becomes more dominant at higher Reynolds numbers.