Estimating the age and strength of beneficial alleles is central to understanding how adaptation proceeds in response to changing environmental conditions. Several haplotype-based estimators exist for inferring the age of segregating beneficial mutations. Here, we develop an approximate Bayesian-based approach that rather estimates these parameters for fixed beneficial mutations in single populations. We integrate a range of existing diversity, site frequency spectrum, haplotype- and linkage disequilibrium-based summary statistics. We show that for strong selective sweeps on de novo mutations the method can estimate allele age and selection strength even in nonequilibrium demographic scenarios. We extend our approach to models of selection on standing variation, and co-infer the frequency at which selection began to act upon the mutation. Finally, we apply our method to estimate the age and selection strength of a previously identified mutation underpinning cryptic colour adaptation in a wild deer mouse population, and compare our findings with previously published estimates as well as with geological data pertaining to the presumed shift in selective pressure.