This paper focuses on developing ambient-cured alkali-activated concrete incorporating recycled concrete aggregates (RA). The binder was either slag or a blend of slag and fly ash (3:1, by mass). Hook-ended steel fibers were added, in 2% volumetric fraction, to improve the properties of concrete made with RA. The alkaline activator solution was a blend of sodium silicate and sodium hydroxide. Concrete mixtures were proportioned to achieve three target compressive strengths, namely 30, 45, and 60 MPa. The performance of concrete mixtures was assessed based on 1, 7, and 28-day compressive strengths. Experimental results showed that full replacement of natural aggregates by RA caused up to 28% reduction in compressive strength of plain alkali-activated slag concretes, with greater reductions being reported in mixtures with higher target strength and tested at 28 days. The incorporation of 2% steel fibers enhanced the strength and caused limited strength reductions of up to 7%. Compared to alkali-activated slag RA concretes, mixtures with 25% fly ash replacement exhibited lower strengths at 1 and 7 days, but their 28-day strength was superior. Analytical multi-linear regression models were developed to identify statistical significance of concrete components and examine their impact on the compressive strength.