Homologous recombination (HR) repairs DNA double-strand breaks (DSBs) in the S and G2 phases of the cell cycle1-3. Several HR proteins are preferentially recruited to DSBs at transcriptionally active loci4-10, but how transcription promotes HR is poorly understood. Here we develop an assay to assess the effect of local transcription on HR. Using this assay, we find that transcription stimulates HR to a substantial extent. Tethering RNA transcripts to the vicinity of DSBs recapitulates the effects of local transcription, which suggests that transcription enhances HR through RNA transcripts. Tethered RNA transcripts stimulate HR in a sequence- and orientation-dependent manner, indicating that they function by forming DNA-RNA hybrids. In contrast to most HR proteins, RAD51-associated protein 1 (RAD51AP1) only promotes HR when local transcription is active. RAD51AP1 drives the formation of R-loops in vitro and is required for tethered RNAs to stimulate HR in cells. Notably, RAD51AP1 is necessary for the DSB-induced formation of DNA-RNA hybrids in donor DNA, linking R-loops to D-loops. In vitro, RAD51AP1-generated R-loops enhance the RAD51-mediated formation of D-loops locally and give rise to intermediates that we term 'DR-loops', which contain both DNA-DNA and DNA-RNA hybrids and favour RAD51 function. Thus, at DSBs in transcribed regions, RAD51AP1 promotes the invasion of RNA transcripts into donor DNA, and stimulates HR through the formation of DR-loops.