We developed a novel synthesis strategy of titania nanowire arrays by employing simple hydrothermal reaction and ion-exchange reaction techniques. Hydrothermal reactions of metallic titanium powder with $H_2O_2$ in a 10 M NaOH solution produced a new sodium titanate compound, $Na_2Ti_6O_{13}{cdot}xH_2O$ (x~4.2), as arrays of nanowires of lengths up to 1 mm. Acid-treatment followed by calcination of this material produced arrays of highly crystalline anatase nanowires as evidenced by x-ray diffraction, Raman spectroscopy, and transmission electron microscopy studies. In both cases of sodium titanate and anatase, the nanowires have exceptionally large aspect ratios of 10,000 or higher, and they form arrays over a large area of $1.5 { imes} 3 cm^2$. Observations on the reaction products with varied conditions indicate that the array formation requires simultaneously controlled formation and crystal growth rates of the $Na_2Ti_6O_{13}{cdot}xH_2O$ phase.