The Fe–Ga body-centered cubic (bcc) alloys within the 15–20 at.% Ga composition range have abnormally high magnetostriction. There is growing evidence that this effect is associated with the magnetic field-induced flip of tetragonal axes of nanoparticles of the ordered phase formed in this range. We studied structural transformations within this composition range at 550 °C by using computer modeling of the atomic-scale ordering and clustering in the atomic density field approximation. It is shown that the initial stage of equilibration of the compositionally homogeneous bcc solid solution with 19 at.% Ga results in bcc → B2 congruent ordering followed by a precipitation of Ga-rich B2 particles, which eventually transform to particles of the DO3 phase. At the composition 21 at.% Ga, the congruently ordered B2 phase undergoes further B2 → DO3 congruent ordering, which is followed by decomposition into an equilibrium mixture of the bcc and DO3 phases. An important result is that the phase transformations at 0.15 < c < 0.19 produce nanoparticles of transient B2 phase. We assume that the nanoprecipitates of the transient B2 phase undergo a diffusionless cubic → tetragonal transformation, forming the L10 phase during cooling to the room temperature, and that this involves a magnetic field-induced flipping of tetragonality of these nanoprecipitates which may be responsible for the giant magnetostriction.