At 0615 GMT, the rand traded at 15.5275 against the U.S. dollar, 0.43% firmer than its previous close on Friday.
The unit was trading at its strongest since March 5, which was before the COVID-19 pandemic knocked the local economy deeper into recession.
Biden crossed the threshold of the 270 electoral college votes required for victory on Saturday by winning the battleground state of Pennsylvania. Republicans appear to have retained control of the Senate, though the final makeup may not be clear until runoff votes in Georgia in January.
"Although the rand has benefited significantly over the course of the most recent sessions, given the extent of the recent gains, we are likely to encounter both profit taking on short U.S. dollar positions and fresh dollar buyers at the current levels," Nedbank analysts said in a note.
The analysts added that although the rand's technical indicators were suggesting an oversold scenario, "indications are that it could extend its gains further towards the 15.0000 level."
Government bonds also firmed, with the yield on the benchmark instrument due in 2030 down seven basis points to 8.900%.
(Reporting by Olivia Kumwenda-Mtambo; Editing by Rashmi Aich)