The atomic and electronic structures of fluorinated BN nanotubes (BNNTs) were investigated by generalized gradient approximation (GGA) density functional theory (DFT). The reaction energies of F-2 with pristine single-walled BNNTs to form fluorinated BNNTs are exothermic up to 50% coverage. At lower F coverages (below 50%), fluorines prefer external attachments to boron atoms and stay as far away as possible. At 50% F coverage, fluorines favor attachment to all the boron atoms of the outer surface energetically. Such preferable fluorination patterns and highly exothermic reaction energies hold true for double-walled (and multiwalled) BNNTs when the outer tube surface is considered. Fluorination transforms BNNTs into p-type semiconductors at low F coverages, while high F coverages convert BNNTs into p-type conductors. Therefore, the electronic and transport properties of BNNTs can be engineered by fluorination, and this provides potential applications for fluorinated BNNTs in nanoelectronics.