Twisted laminar superconducting composite structures based on multi-wall carbon nanotube (MWCNT) yarns were crafted by integrating magnesium and boron homogeneous mixture into the carbon nanotube (CNT) aerogel sheets. After the ignition of the Mg–B–MWCNT system, under the controlled argon environment, the high exothermic reaction between magnesium (Mg) and boron (B) with stoichiometric ratio produced the MgB$_2$@MWCNT superconducting composite yarns. The process was conducted under the controlled argon environment and uniform heating rate in the differential scanning calorimetry and thermogravimetric analyzer. The XRD analysis confirmed that the produced composite yarns contain nano and microscale inclusions of superconducting phase of MgB$_2$. The mechanical properties of the composite twisted and coiled yarns at room temperature were characterized. The tensile strength up to 200 MPa and Young’s modulus of 1.27 GPa proved that MgB$_2$@MWCNT composite is much stiffer than single component MgB$_2$ wires. The superconductive critical temperature of T$_c$ ${\sim}$38 K was determined by measuring temperature-dependent magnetization curves. The critical current density, J$_c$ of superconducting component of composite yarns was obtained at different temperatures below T$_c$ by using magnetic hysteresis measurement. The highest value of J$_c$ = 3.39 9 10$^7$A cm$^{-2}$ was recorded at 5 K.