The Blues agreed a £30.5million fee for the forward on Thursday, with Madueke travelling to London to complete a medical and sign his seven-and-a-half-year Chelsea contract.
That has all now been completed, with the 20-year-old the sixth player to join the club in the January window.
Chelsea announced the deal by pointing towards a link in the Twitter bio to Madueke’s Instagram account.
“I’m really pleased to sign with one of the best clubs in the world in Chelsea,” Madueke told the club website.
“To return to England and play in the Premier League is a dream for me and my family and I can’t wait to get started. I am excited for what the future holds, the owner's vision for the future and to be at a club like this and winning at the highest level.”
Madueke follows Mykhailo Mudryk, David Datro Fofana, Andrey Santos and Benoit Badiashile in making a permanent move to Stamford Bridge, while Joao Felix has also arrived on loan.
It takes Chelsea’s January spending beyond the £150m mark and they have now spent more than £450m on players under the new ownership of Todd Boehly and Behdad Eghbali.
A statment from chairman Boehly and co-controlling owner Behdad Eghbali read: “We're delighted to bring Noni to Chelsea.
“He’s an exciting talent who has proven his quality over the past few years with PSV, playing in a strong European league, and we are thrilled he has chosen to join Chelsea for this next stage of his career. We are sure he will form an important part of our team.”
Madueke has made just two Eredivisie starts this season for PSV due to injury problems, and only came off the bench in the club’s two Europa League matches against Arsenal.
The forward spent four years at Tottenham as a youngster, and has four England U21 caps to his name.
The club stated: “Chelsea would like to thank PSV for their cooperation in enabling Noni to take up this new opportunity.”