Computational thinking (CT) learning activities are increasingly integrated in early-stage school curricula in several countries. Tools used to teach CT in early school years include unplugged coding—i.e., programming without computing devices—and educational robotics (ER)—i.e., giving instructions to a digitally controlled mechanical robot to perform specific actions in a physical environment. Past studies have shown that training coding skills through ER enhances first graders’ executive functions (EFs). Little is known, however, about the effects of ER interventions, alone or combined with un-plugged activities, on preschoolers’ CT and EF skills. In a cluster-randomized controlled trial, we assessed whether improvements in preschoolers’ coding skills, following interventions based on combinations of unplugged coding and ER, transfer to plugged (computer-based) coding abilities and to EFs such as planning, response inhibition, and visuo-spatial skills. Forty-seven preschoolers from four class groups, with no prior exposure to coding, were randomly assigned to an experimental (unplugged coding and ER, two classes) or control (standard school activities, two classes) instructional groups. Four coding tasks, one standardized planning task (Tower of London test), one standardized response inhibition task (NEPSY-II inhibition subtest), and one visuo-spatial standardized task (Primary Mental Ability subtest) were used to assess children’s skills at the pretest (before the intervention) and posttest (after the intervention). To measure retention, the same skills were also assessed for 22 children from the experimental group 3 months from the posttest (follow up). The paper discusses the results of this experimental intervention. The results show significant positive effects of the instructional program on children’s computer-based coding skills and cognitive abilities, particularly visuo-spatial skills. Between pretest and posttest, children in the experimental group improved in coding, z = 3.84, p = 0.000, r = 0.87, and in visuo-spatial skills, z = 3.09, p = 0.002, r = 0.69. The waiting list control group showed improvements in coding skills only after the intervention, at the assessment point T3, z = 2.99, p = 0.003, r = 0.71. These findings show that practice with tangible and unplugged coding during the last year of preschool not only significantly improves children’s skills to solve computer-based coding problems (near-transfer effect), but it may also have some far-transfer effects on cognitive functions, such as visuo-spatial skills.