The structural, electronic and magnetic properties of transition metal TM (TM = Fe and Co) monatomic nanochains encapsulated inside and between (6,6) boron nitride nanotube (BNNT) bundle have been investigated by the first-principles calculations in the framework of the density functional theory. Our results show that intercalation of TM chains leads to the significant changes in the geometrical structure. All TM chains TM-Chs@BNNT bundle systems have negative formation energy so they are stable and exothermic. It is found that all these TM-Chs@BNNTs bundle systems are ferromagnetic and a spin splitting between spin up and down is observed. The spin polarization and the magnetic moment of the systems depend on the position and the type of the transition metal atomic chains.