Black phosphorus (BP) has been shown as a promising two‐dimensional (2D) material for electronic devices owing to its high carrier mobility. To realize complementary electronic circuits with 2D materials, it is important to fabricate both n‐type and p‐type transistors with the same channel material. By engineering the contact region with copper (Cu)‐doped BP, here we demonstrate an n‐type carrier transport in BP field‐effect transistors (FETs), which usually exhibit strongly p‐type characteristics. Cu metal atoms are found to severely penetrate into the BP flakes, which forms interstitial Cu (Cuint)‐doped edge contact and facilitates the electron transport in BP. Our BP FETs in back‐gated configuration exhibit n‐type dominant characteristics with a high electron mobility of ~ 138 cm2 V−1 s−1 at room temperature. The Schottky barrier height for electrons is relatively low because of the edge contact between Cuint‐doped BP and pristine BP channel. The contact doping of BP by highly mobile Cu atoms gives rise to n‐type transport property of BP FETs. Furthermore, we demonstrate a p‐n junction on the same BP flake with asymmetric contact. This strategy on contact engineering can be further extended to other 2D materials.