Measurements of differential cross sections dσ/dϕ * and double-differential cross sections d(^{2}) σ/dϕ *d|y| for inclusive Z boson production are presented using the dielectron and dimuon final states. The kinematic observable ϕ * correlates with the dilepton transverse momentum but has better resolution, and y is the dilepton rapidity. The analysis is based on data collected with the CMS experiment at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 19.7 fb⁻¹. The normalised cross section (1/σ) dσ/dϕ *, within the fiducial kinematic region, is measured with a precision of better than 0.5% for ϕ * < 1. The measurements are compared to theoretical predictions and they agree, typically, within few percent.