While photosynthetic responses to elevated CO2, elevated temperature, or water availability have previously been reported for grapevine as responses to single stress factors, reports on the combined effect of multiple stress factors are scarce. In the present work, we evaluated effects of simulated climate change [CC; 700 ppm CO2, 28/18 °C, and 33/53% relative humidity (RH), day/night] versus current conditions (375 ppm CO2, 24/14 °C, and 45/65% RH), water availability (well-irrigated vs. water deficit), and different types of soil textures (41, 19, and 8% of soil clay contents) on grapevine (Vitis vinifera L. cv. Tempranillo) photosynthesis. Plants were grown using the fruit-bearing cutting model. CC increased the photosynthetic activity of grapevine plants grown under well-watered conditions, but such beneficial effects of elevated CO2, elevated temperature, and low RH were abolished by water deficit. Under water-deficit conditions, plants subjected to CC conditions had similar photosynthetic rates as those grown under current conditions, despite their higher sub-stomatal CO2 concentrations. As expected, water deficit reduced photosynthetic activity in association with inducing stomatal closure that prevents water loss. Evidence for photosynthetic downregulation under elevated CO2 was observed, with decreases in photosynthetic capacity and leaf N content and increases in the C/N ratio in plants subjected to CC conditions. Soil texture had no marked effects on photosynthesis and did not modify the photosynthetic response to CC and water-deficit conditions. However, in mature well-irrigated plants grown in the soils with the highest sand content, an important decrease in stomatal conductance was observed as well as a slight decrease in the utilization of absorbed light in photosynthetic electron transport (measured as photochemical quenching), possibly related to a low water-retention capacity of these soils even under well-watered conditions.