What you are interested in is the color temperature rating, rated in Kelvins.
Lower K rating is redder (2700K Warm White), higher is bluer (5000K Daylight).
LEDs and fluorescent tubes use phosphor technology to produce the light and by changing the phosphor mix, unlike other lighting, can be made available a wider range of Kelvin ratings.
If you're already using T-8 (1" dia), T-5 (5/8" dia) or T-4 (1/2" dia) tubes, you might get by just by changing the tubes out from the Cool White or Daylight color you describe for Warm White.
I wouldn't bother if you have T-12 (1.5" dia) tubes, these bulky old, larger tubes require more power in both the ballast and the tube to produce light. Best to swap to LED lighting, pricing has come down and the fixtures are a lot smaller.
Kelvin ratings of common lighting:
- Candle 1800K
- Tungsten Incandescent 2700-2800K
- Tungsten Quartz Halogen 3200K
- Cool White Fluorescent 4300K
- Bright Sunlight 5600K
Standard 4 ft T8 Warm White - F32-T8-827
Note: Technically, there are two types of LED systems out there, Native color LEDs that emit a certain color of light due to the elemental makeup of their PN junction and White Light LEDs that emit UltraViolet light and use phosphors embedded in their plastic casings that fluoresce in the visible spectrum to convert it to perceived white light. The first are specified by the nanometer light wavelength emitted (color), the second by their Kelvin rating.
White Light Phosphor LEDs most closely approximate the spectrum of lighting we are already acquainted with.