Congratulations! Yes he will certainly be much happier in there!
Hey, don't let anyone tell you that you absolutely need 5 gallons for a Betta! As long as you give him proper care (enough water changes and a heater) he'll be perfectly happy in those 3 gallons!
I do have a suggestion though: Plants! lol even if they are silk, he'd love some places to hide in and play in all day! Betta's especially love to weave in and out of plants
But it looks great!
EDIT: to shellieca, I can see the filter is from the 1 gallon Minibow (I've got the same one) of course this is just me assuming the OP hasn't changed the media, but it is at least from the original bowl so if they haven't rinsed it, it should still be holding some BB.