It'll probably take atleast 2 to 3 weeks. Also, it may take a month. Not all budgies are the same, the more you give him nutricious things, the more stronger he will be, and lastly, will be able to grow his wings.
You will have to wait until his next moult for them to grow back and most budgies moult every 4-6 months It really just depends on when he had his last one and when he decides to start the next. As Kat said when he does moult be sure to give him lots of extra good food!
I am in the same boat with Pekoe. When we bought her they had someone do a total hack job on the wings! She's moulting now, but no sign of big feathers yet
I've been giving her lots of floor time and she's been learning how to use these wings and can go quite a distance and height now.
I had Winter's wings clipped at the store before I brought him home, but they clipped it a bit too much. It took Winter over 3 and a half months to start flying all around my room and get on top of the curtain rod...that was after around 2.5 months after he finished his first moult.