Catalyzes the transfer of electrons from NADPH to thioredoxins TRX1, TRX2 and TRX3, which in turn act as reductants of disulfide containing proteins (PubMed:9368022, PubMed:11013257, PubMed:16910770, PubMed:23845423). Able to reduce nitroglutathione (GSNO), a compound involved in the transport of nitric oxide (NO); however, TRX1 is more efficient in reducing GSNO (PubMed:11013257). Has no catalytic activity towards oxidized glutathione (GSSG) (PubMed:11013257). [thioredoxin]-dithiol + NADP(+) = [thioredoxin]-disulfide + H(+) + NADPH Binds 1 FAD per subunit. kcat is 1725 min(-1) with TRX1 as substrate (at pH 7.4) (PubMed:23845423). kcat is 51.7 sec(-1) with TRX1 as substrate (at 25 degrees Celsius and at pH 7.4) (PubMed:23845423). kcat is 275.2 min(-1) with NADPH and DTNB as substrates (at pH 7.4) (PubMed:9368022). kcat is 48.3 sec(-1) with NADPH and TRX1 as substrates (at 25 degrees Celsius and at pH 7.4) (PubMed:11013257). kcat is 9.4 min(-1) with nitrosoglutathione (GSNO) as substrates (at 25 degrees Celsius and at pH 7.4) (PubMed:11013257). Homodimer. Produced by alternative initiation at Met-77 of isoform 1. In Plasmodium, the C-terminal redox center, which acts as the active site, is formed by two cysteines while in mammalian TRXR this redox center is composed of a cysteine-selenocysteine active site. Belongs to the class-I pyridine nucleotide-disulfide oxidoreductase family.