The Nigeria international passed a medical with the Foxes earlier this week and agreed terms on a five-and-a-half-year deal.
Ndidi, likened in style to former Leicester ace N'Golo Kante, has now been given the all-clear to feature for City in this weekend's FA Cup tie with Everton after taking part in training with his new teammates for the first time on Thursday.
"Everything with the work permit is OK," manager Claudio Ranieri told reporters. "He trained today. He is available for Saturday and all is fine. I don't know [if he will play]. Let me see him in training. Today was his first session. He was OK and I want to see tomorrow and then I'll choose.
"He is a very impressive player with a great future. He is tall and jumps very well for the headers, moves the ball quickly and recovers the ball very well.
"We have followed him a lot and we hope he will very quickly impress the fans. He's another kind of player [to Kante] - totally different. A lot of big teams wanted him, but he prefers to come with us to improve."
Jamie Vardy is also in contention to feature for the Premier League champions at Goodison Park after completing a three-game ban, while Islam Slimani is likely to recover from illness in time to be considered for selection.