We report fabrication of silica convex microlens arrays with controlled shape, size, and curvature by femtosecond laser direct writing. A backside etching in dye solution was utilized for laser machining high-fidelity control of material removal and real-time surface cleaning from ablation debris. Thermal annealing was applied to reduce surface roughness to 3 nm (rms). The good optical performance of the arrays was confirmed by focusing and imaging tests. Complex 3D micro-optical elements over a footprint of $ 100 \times 100\;\unicode{x00B5}{{\rm m}^2} $100×100µm2 were ablated within 1 h (required for practical applications). A material removal speed of $ 120\;\unicode{x00B5}{{\rm m}^3}/{\rm s} $120µm3/s ($ 6 \times {10^5} \;{{\rm nm}^3}/{\rm pulse} $6×105nm3/pulse) was used, which is more than an order of magnitude higher compared to backside etching using a mask projection method. The method is applicable for fabrication of micro-optical components on transparent hard materials.