We have constructed 23‐year (1994–2016) time series of Antarctic Peninsula (AP) ice‐shelf height change using data from four satellite radar altimeters (ERS‐1, ERS‐2, Envisat, and CryoSat‐2). Combining these time series with output from atmospheric and firn models, we partitioned the total height‐change signal into contributions from varying surface mass balance, firn state, ice dynamics, and basal mass balance. On the Bellingshausen coast of the AP, ice shelves lost 84 ± 34 Gt a$^{-1}$ to basal melting, compared to contributions of 50 ± 7 Gt a$^{-1}$ from surface mass balance and ice dynamics. Net basal melting on the Weddell coast was 51 ± 71 Gt a$^{-1}$. Recent changes in ice‐shelf height include increases over major AP ice shelves driven by changes in firn state. Basal melt rates near Bawden Ice Rise, a major pinning point of Larsen C Ice Shelf, showed large increases, potentially leading to substantial loss of buttressing if sustained.