I want to create a blurred gradient background effect similar to the designs below. How can I do this using Inkscape or Photoshop/Illustrator?
Could be a simple gradient in Illustrator. If one wishes more control, then a Gradient Mesh may help.
For Photoshop one just uses the Gradient Tool with subtle foreground/background colors and click-drags.
The key is to use subtle color changes. In these images the difference between the dark (black) and the color is minute, merely reducing the amount of black (or increasing saturation) so more of the color shows.