You can buy led light fixtures that are very similar to size and shape of the florescent fixtures. My mom recently had about three replaced. You can purchase them at any big box store. If yours are wired in you may have to have a outlet to plug them in instead of hardwired. I guess if you are just looking into keeping the same light set up you have. The units do not have replaceable bulbs or anything, the fixture and led lights are all one unit.

We need different photos. Stand back & shoot new ones so we have some context. Also, post the dimensions of the openings.

They also make LED tubes that are direct replacements for fluorescents. Some need the (electronic, not magnetic) ballast to stay in place and be functional, some need the ballast to be removed. I have never seen them at big box stores, but lighting and electrical supply houses in my area have them readily available in different colour temperatures.

Unless there are special circumstances, I'd strongly recommend just replacing the fixture with an LED fixture. They're widely available and not expensive (although of course you can go more elaborate and expensive if you wish). Fixtures are available that wire directly in (no outlet needed). Replacing is as simple as turning off power, removing fixture from ceiling/detaching wiring, attaching wires and fixing to ceiling.

I replaced a few recently and looked into converting the fluorescent fixtures to LED - it was frankly easier and cleaner and simpler to replace the whole thing. Converting a fixture is not complicated but there are some catches (ballast type, bulb type, wiring specifics for different bulbs, etc). And on top of that, some of the old fixtures had deteriorated or been broken, and in process of removing and taking apart to convert you may well end up with a mess (old plastic parts may be brittle and other problems).

I ended up removing one good fixture - replacing with a smaller and nicer LED fixture - and moving the old one to replace a partly-broken one in a little-used room. The remaining fluorescents I'll replace over time as the bulbs burn out. One other fixture in very bad shape I replaced with an entirely new fixture that takes LED tubes - it was only slightly more expensive than buying the tubes alone (i.e. converting the old fixture would have been a huge waste of time and prone to type mismatches, even if it was still in working order).

Quality of light and performance is far better - they don't buzz, they turn on immediately, they don't flicker, and they use about half as much electricity.

Note, fluorescents have mercury and other toxics and have to be properly disposed of - another reason why I'll be happy to be rid of them.

LEDs are a great solution for many cases, but check the labels for efficacy. Many of them, especially cheaper ones, are in the 50-60 lumens per watt range.

Some LED fixtures, especially the low end ones, may not even be as cheap to operate as you'd expect, or as their wattage rating suggests. That's because these cheapies have poor power factor. In the past, power factor didn't really matter for residential use -- power meters ignored it. However, I've read that some utilities using "smart" meters are starting to charge you extra for poor power factor, if the utility enables that "feature." (I'm simplifying here, but that's what it amounts to.)

In recent years, fluorescents have gone out of fashion. That's too bad, because in the last couple of decades, they've been vastly improved.

Well designed modern electronic fluorescent ballasts don't buzz or hum. There's no flicker, because they operate at high frequencies. They strike the lamps immediately (that's why they're called instant start ballasts). With linear T5 or T8 lamps, they're as efficient as any mass market LED fixture or retrofit, and better than many, typically 90-100 lumens per watt.

While retrofit (screw-base) compact fluorescents have rightly given way to better LED retrofits, dedicated linear fluorescent fixtures can still be an outstanding choice for areas where you want smooth, even, low-shadow lighting. I'm still using most of mine, upgraded with modern ballasts and T8 lamps, and I've even installed some new ones within the last couple of years.

Just some thoughts.

@DavidR - thanks, you make some good points. Fluorescents have improved and they do make sense for some applications and they're pretty efficient (it's not a big gain like swapping out incandescent bulbs). I still think that if swapping out older fixtures LEDs make more sense most of the time, but it's not always the case. And I'd particularly say that if someone has a recent, high quality fluorescent fixture that they're happy with, just replacing the bulbs may well make more sense and be more economical (and some will be happy converting older fixtures). My case - probably not rare, but not universal - was mostly swapping older fixtures. And I'm mostly leaving the old fixtures in place until they die, but where I am renewing or replacing, LEDs just make more sense.

I have converted several old fluorescent fixtures to use the linear LED tubes. I went the 'remove the ballast' route. (Sick & tired of dealing with ballasts &, IIRC, if using the direct replacement, leave the ballasts wired, the ballast still consumes power, making it a less energy efficient choice. Plus probable future ballast problems.)

If OP opts to keep the fixture, swivel end linear LED's will be needed (I think*) so the light can be directed. Linear LED tubes do not have omni-directional light like fluorescent tubes.

*Still confused about the situation; can't make sense out of the posted photos because I can't see how they relate to the room as a whole. I suspect that the thin panel drop-in LED panels would be a better solution. Would be a cleaner look and would eliminate the need for the egg crate covers.

Linear LED tubes do not have omni-directional light like fluorescent tubes.

That's the problem with LEDs in general. They're directional. That's somewhat limiting for area lighting.

The way to overcome this has been to use diffusers and lots and lots of LEDs, a brute force approach made possible mostly by the very low cost of Chinese LED mass manufacturing.

Fluorescent lighting is naturally more even and shadow-free, because of the large surface area that emits light.

I do see an LED solution to this, though, and that's the relatively new COB (chip on board) LED design. Instead of a few dozen individual chips or plastic packaged LEDs soldered to a printed circuit board, COB designs allow for hundreds or thousands of tiny LEDs on a single substrate. They combine to give something much closer to the even wash of light you get from good fluorescents.

I'm a little concerned about reliability with COB, though. We'll see how that shakes out.

Not really directly related to original question, but I'm going to contradict myself about converting existing fixtures to LEDs. I have a bunch of older fixtures in a garage and ended up with an extra from replacing a fixture elsewhere, so converted it to give it a try. Although I'm an electrical novice, it was dead easy with a bit of thought - mainly ripping out the ballasts and starters and all the excess wiring since the LED layout much simpler. Rather a pleasant task easily done while listening to radio or whatever. And now I have some spare parts (starters in particular) that have already come in handy to fix some flickering tubes - given the age of these things, also needed.

But the really big advantage is that I don't have to remove and replace the fixture bases. Or to be exact, drill holes in concrete to attach new ones and all that tedious stuff. The old ones don't look particularly attractive, but it's a garage. LEDs a big improvement but comparing to old ones perhaps not fair.

Anyway a case where converting can make sense. I'll probably do the remaining ones over time.