Identification of jets originating from beauty and charm quarks is important for measuring Standard Model processes and for searching for new physics. The performance of algorithms developed to select $b$- and $c$-quark jets is measured using data recorded by LHCb from proton-proton collisions at $\sqrt{s}=7$ TeV in 2011 and at $\sqrt{s}=8$ TeV in 2012. The efficiency for identifying a $b(c)$ jet is about 65%(25%) with a probability for misidentifying a light-parton jet of 0.3% for jets with transverse momentum $p_{\rm T} > 20$ GeV and pseudorapidity $2.2 < \eta < 4.2$. The dependence of the performance on the $p_{\rm T}$ and $\eta$ of the jet is also measured.