The Blues had made the 20-year-old a top target over the January transfer window and have moved quickly to secure his services ahead of Leeds United and Tottenham.
Madueke flew into London on Thursday night ahead of a medical and to finalise personal terms with the Premier League club.
He will need to have completed the move by midday on Friday to feature against Liverpool on Saturday.
Madueke has been regarded as one of the top talents across Europe and started off his career at the academies of Crystal Palace and Tottenham.
Graham Potter has had a torrid time at Stamford Bridge in recent weeks but new owners Todd Boehly and Behdad Eghbali have backed the English coach in the January transfer window.
Madueke will become the sixth arrival at the club this month after Mykhailo Mudryk, Andrey Santos, Benoit Badiashile, David Datro Fofana and Joao Felix.
The deal will take Chelsea’s spending in the January window to £190m, adding to the £270m spent in the summer to make it £460m in outlays since Todd Boehly took over the club.
Work behind the scenes from new transfer chiefs Christopher Vivell and Paul Winstanley have seen the Blues make rapid progress in the transfer window while the current crop might be shifted on.
However, Madueke’s injury troubles might simply add to Chelsea’s woes this season and the England Under-21 international has made just two starts in the Eredivisie this campaign after an ankle injury kept him out for most of the year.
Potter has had to juggle an injury crisis in the past month with Reece James, Ben Chilwell, Wesley Fofana, N’Golo Kante, Denis Zakaria, Pulisic and Sterling all sidelined.
But the Stamford Bridge chiefs believe signing Madueke now is a risk worth taking as his value could have skyrocketed had he fulfilled his potential at PSV.
How Potter will assemble his expensive squad remains to be seen with Madueke already joining a long list of attackers at the club now.
It was only last week when Mudryk was pinched from under Arsenal’s noses and the 22-year-old is another top talent with a big future ahead of him.
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