The glucagon-like peptide-1 receptor (GLP-1R) is an important regulator of blood glucose homeostasis. Ligand-specific differences in membrane trafficking of the GLP-1R influence its signalling properties and therapeutic potential in type 2 diabetes. Here, we have evaluated how different factors combine to control the post-endocytic trafficking of GLP-1R to recycling versus degradative pathways. Experiments were performed in primary islet cells, INS-1 832/3 clonal beta cells and HEK293 cells, using biorthogonal labelling of GLP-1R to determine its localisation and degradation after treatment with GLP-1, exendin-4 and several further GLP-1R agonist peptides. We also characterised the effect of a rare GLP1R coding variant, T149M, and the role of endosomal peptidase endothelin-converting enzyme-1 (ECE-1), in GLP1R trafficking. Our data reveal how treatment with GLP-1 versus exendin-4 is associated with preferential GLP-1R targeting towards a recycling pathway. GLP-1, but not exendin-4, is a substrate for ECE-1, and the resultant propensity to intra-endosomal degradation, in conjunction with differences in binding affinity, contributes to alterations in GLP-1R trafficking behaviours and degradation. The T149M GLP-1R variant shows reduced signalling and internalisation responses, which is likely to be due to disruption of the cytoplasmic region that couples to intracellular effectors. These observations provide insights into how ligand- and genotype-specific factors can influence GLP-1R trafficking.