Background: Older adults improve their cognitive performance on a target task after succeeding in a prior task. We tested whether effects of prior-task success occur via changing older adults’ ability to select the better strategy and/or to execute strategies efficiently. Methods: Young and older participants (n = 162) accomplished a computational estimation task (i.e., providing the best estimates to arithmetic problems) after accomplishing a dot comparison task. Results: Both groups increased their performance on computational estimation following success on dot comparison. Older adults improved most and outperformed young adults following prior-task success. Prior-task success led older adults to select the better strategy more often and to repeat (or not) the same strategy more often when it was appropriate. Better strategy use mediated effects of prior-task success. Individual differences in baseline performance moderated individuals’ sensitivity to effects of prior-task success. Conclusion: Our findings further our understanding of mechanisms underlying effects of prior-task success and provide new perspectives on how social environment modulates age-related differences in cognitive performance.