I've gotten a couple new budgies very recently.
I can give you advice that the others on this site have been kind enough to give me.
I had one to start with and she didn't eat or drink anything.
She was very lonely because she'd grown up around many many birds.
Since yours is eating maybe you'll be okay. Budgies are supposed to be kept in at least 2s though. I thought I could make it work with just 1 too, but she was too sad and it broke my heart.
What're you giving him to drink out of? I've been told covered containers, or ones placed at the bottom of the cage are too scary for birds placed in a new environment to start with, as they can't look for predators.
Put the water up by it's favourite perch(generally the highest one in the cage), it might encourage it.
I've also been told it's common for most budgies to do a lot of drinking in the morning. Maybe people have only seen their budgies drinking 2-3 times in the years they've had them, so he could be drinking without you knowing.