TL;DR
Yes, once they're ripe. Refrigeration slows spoilage but also dulls flavor and softens texture, so timing matters more than the yes or no.
Tomatoes get conflicting advice because the right answer changes depending on ripeness. An unripe tomato behaves completely differently in the fridge than one that's already soft and ready to eat.
The science comes down to temperature and enzyme activity. Cold slows the chemical reactions that both ripen tomatoes and eventually break them down, which is exactly why timing matters so much here.
Unripe vs ripe tomatoes
Green or firm tomatoes should stay on the counter, ideally out of direct sun, until they fully ripen, which usually takes a few days to a week depending on starting color. Temperatures below about 55°F (13°C) slow or stall the ripening enzymes, so a fridge can leave an unripe tomato stuck mealy and underdeveloped instead of ripening properly the way it would at room temperature.
How long the fridge actually helps
Once a tomato is ripe, refrigeration can add roughly 5-7 extra days of usable life compared to leaving it on the counter, where ripe tomatoes typically last only 2-3 days before going soft or moldy. That extension matters most if you've bought more than you'll use in the next couple of days, or if a heat wave has your kitchen running warmer than usual.
What cold does to flavor and texture
Below about 55°F, tomato cell membranes break down in ways that make the flesh mealy and mute the volatile compounds responsible for that classic tomato aroma. This is why a chilled tomato can taste flat and grainy straight out of the fridge, even though nothing is technically wrong with it. Letting it sit at room temperature for 20-30 minutes before eating brings back noticeably more flavor and juiciness, since those aroma compounds become more active again as the fruit warms.
Storing cut tomatoes
Once a tomato is cut, refrigeration isn't optional; bacteria multiply fast on the exposed flesh at room temperature. Store cut tomatoes in a covered container in the fridge and use them within about 2 days.
A middle-ground option
If you're short on counter space or worried about fruit flies, some people ripen tomatoes on the counter and only move them to the fridge for the last day or two before use, getting a bit of extra shelf life without sacrificing much flavor. Whatever approach you use, avoid storing tomatoes in a sealed plastic bag at any stage; they need some airflow, and trapped humidity speeds up mold rather than preventing it. Storing them stem-side down also helps, since it slows moisture loss through the scar where the tomato was picked and can add a day or two of usable life either on the counter or in the fridge.
Let tomatoes ripen on the counter, then move them to the fridge only if you need extra days. Pull them out ahead of time and they'll taste close to fresh.