Two dimensional (2D) ferromagnetic materials have attracted much attention in the fields of condensed matter physics and materials science, but their synthesis is still a challenge given their limitations on structural stability and susceptibility to oxidization. MAX phases nanolaminated ternary carbides or nitrides possess a unique crystal structure in which singleatom-thick "A" sublayers are interleaved by two dimensional "MX" slabs, providing nanostructured templates for designing 2D ferromagnetic materials if the non-magnetic "A" sublayers can be substituted replaced by magnetic elements. Here, we report three new ternary magnetic MAX phases (Ta2FeC, Ti2FeN and Nb2FeC) with "A" sublayers of single-atom-thick 2D iron through an isomorphous replacement reaction of MAX precursors (Ta2AlC, Ti2AlN and Nb2AlC) with a Lewis acid salts (FeCl2). All these MAX phases exhibit ferromagnetic (FM) behavior. The Curie temperature (Tc) of Ta2FeC and Nb2FeC MAX phase are 281 K and 291 K, respectively, i.e. close to room temperature. The saturation magnetization of these ternary magnetic MAX phases is almost two orders of magnitude higher than that of V2(Sn,Fe)C MAX phase whose A-site is partial substituted by Fe. Theoretical calculations on magnetic orderings of spin moments of Fe atoms in these nanolaminated magnetic MAX phases reveal that the magnetism can be mainly ascribed to intralayer exchange interaction of the 2D Fe atomic layers. Owning to the richness in composition of MAX phases, there is a large compositional space for constructing functional single-atom-thick 2D layers in materials using these nanolaminated templates.