The FDA has approved four tests for COVID-19 antibodies. Here are links provided by the FDA for these tests.
Cellex – a lateral flow immunoassay for qualitative detection of antibodies (IgM and IgG) https://www.fda.gov/media/136625/download
Ortho Clinical Diagnostics- immunoassay using horseradish peroxidase labeled antigen luminescent reaction where the light emitted is correlated with the presence of antibodies. https://www.fda.gov/media/136967/download
Chembio Diagnostics Systems – a lateral flow immunoassay for qualitative detection of antibodies (IgM and IgG) https://www.fda.gov/media/136963/download
Mount Sinai laboratory https://www.fda.gov/media/137029/download