Dehydration or desiccation is one of the most frequent and severe challenges to living cells. The bacterium Deinococcus radiodurans is the best known extremophile among the few organisms that can survive extremely high exposures to desiccation and ionizing radiation, which shatter its genome into hundreds of short DNA fragments. Remarkably, these fragments are readily reassembled into a functional 3.28-megabase genome. Here we describe the relevant two-stage DNA repair process, which involves a previously unknown molecular mechanism for fragment reassembly called `extended synthesis-dependent strand annealing' (ESDSA), followed and completed by crossovers. At least two genome copies and random DNA breakage are requirements for effective ESDSA. In ESDSA, chromosomal fragments with overlapping homologies are used both as primers and as templates for massive synthesis of complementary single strands, as occurs in a single-round multiplex polymerase chain reaction. This synthesis depends on DNA polymerase I and incorporates more nucleotides than does normal replication in intact cells. Newly synthesized complementary single-stranded extensions become `sticky ends' that anneal with high precision, joining together contiguous DNA fragments into long, linear, double-stranded intermediates. These intermediates require RecA-dependent crossovers to mature into circular chromosomes that comprise double-stranded patchworks of numerous DNA blocks synthesized before radiation, connected by DNA blocks synthesized after radiation.