Management of toxic elements contaminated upland and wetland soils using biochar is of great concern from both agricultural and environmental points of view. The impact of rice straw- and rapeseed residue-derived biochars produced under 300 °C and 550 °C (added to the soil at 2% and 5%; w/w) on the geochemical fractions, phytoavailability, and uptake of Cu and Pb in a contaminated mining soil under different moisture contents (80%, 60%, and 40% of soil field capacity) was investigated in a greenhouse pot experiment using maize. The higher rate of rice straw-derived biochar pyrolyzed at 550 °C caused a significant reduction in the mobile (soluble + exchangeable) fraction of Cu (59.42%) and Pb (75.4%) and increased the residual fractions of Cu (37.8%) and Pb (54.7%) in the treated soil under the highest moisture content (80%) as compared to the untreated soil. Therefore, this biochar significantly decreased the phytoavailability (CaCl-extractable form) of Cu by 59.5% and Pb by 67.6% under the highest moisture content. Also, at the same moisture level (80%), the higher rate of rapeseed residue-derived biochar pyrolyzed at 550 °C decreased significantly the phytoavailability of Cu by 46.5% and Pb by 60.52% as compared to the untreated soil. The 5% rate of the higher temperature pyrolyzed rice straw and rapeseed biochars decreased the uptake of Cu and Pb by the roots and shoots of maize up to 51% for Cu and 45% for Pb. Immobilization of Cu and Pb in the biochar-treated soil at 80% moisture content may possibly due to the associated increase of soil pH and poorly-crystalline Fe oxides content, and/or the metals precipitation with sulfides. These results indicated that application of high temperature pyrolyzed rice straw- and rapeseed residue-derived biochars at 5% could immobilize Cu and Pb and decrease their uptake by maize under high levels of moisture content; consequently, they can be used for phyto-management of Cu and Pb contaminated wetland soils.