Proteases encoded by SARS-CoV-2 constitute a promising target for new therapies against COVID-19. SARS-CoV-2 main protease (Mpro, 3CLpro) and papain-like protease (PLpro) are responsible for viral polyprotein cleavage—a process crucial for viral survival and replication. Recently it was shown that 2-phenylbenzisoselenazol-3(2H)-one (ebselen), an organoselenium anti-inflammatory small-molecule drug, is a potent, covalent inhibitor of both the proteases and its potency was evaluated in enzymatic and antiviral assays. In this study, we screened a collection of 34 ebselen and ebselen diselenide derivatives for SARS-CoV-2 PLproand Mproinhibitors. Our studies revealed that ebselen derivatives are potent inhibitors of both the proteases. We identified three PLproand four Mproinhibitors superior to ebselen. Independently, ebselen was shown to inhibit the N7-methyltransferase activity of SARS-CoV-2 nsp14 protein involved in viral RNA cap modification. Hence, selected compounds were also evaluated as nsp14 inhibitors. In the second part of our work, we employed 11 ebselen analogues—bis(2-carbamoylaryl)phenyl diselenides—in biological assays to evaluate their anti-SARS-CoV-2 activity in Vero E6 cells. We present their antiviral and cytoprotective activity and also low cytotoxicity. Our work shows that ebselen, its derivatives, and diselenide analogues constitute a promising platform for development of new antivirals targeting the SARS-CoV-2 virus.