We analyzed 16 years of GPS and 17 years of Doppler orbitography and radiopositioning integrated by satellite (DORIS) data at continuously operating geodetic sites in Africa and surroundings to describe the present‐day kinematics of the Nubian and Somalian plates and constrain relative motions across the East African Rift. The resulting velocity field describes horizontal and vertical motion at 133 GPS sites and 9 DORIS sites. Horizontal velocities at sites located on stable Nubia fit a single plate model with a weighted root mean square residual of 0.6 mm/yr (maximum residual 1 mm/yr), an upper bound for plate‐wide motions and for regional‐scale deformation in the seismically active southern Africa and Cameroon volcanic line. We confirm significant southward motion ( ∼ 1.5 mm/yr) in Morocco with respect to Nubia, consistent with earlier findings. We propose an updated angular velocity for the divergence between Nubia and Somalia, which provides the kinematic boundary conditions to rifting in East Africa. We update a plate motion model for the East African Rift and revise the counterclockwise rotation of the Victoria plate and clockwise rotation of the Rovuma plate with respect to Nubia. Vertical velocities range from − 2 to +2 mm/yr, close to their uncertainties, with no clear geographic pattern. This study provides the first continent‐wide position/velocity solution for Africa, expressed in International Terrestrial Reference Frame (ITRF2008), a contribution to the upcoming African Reference Frame (AFREF). Except for a few regions, the African continent remains largely under‐sampled by continuous space geodetic data. Efforts are needed to augment the geodetic infrastructure and openly share existing data sets so that the objectives of AFREF can be fully reached.