The forward is set to become the 15th signing of the Todd Boehly-Clearlake Capital era after the Blues agreed a £30.5m fee with the Eredivisie giants.
An England Under-21 international, the 20-year-old has seen his season disrupted by injury and has featured in only nine games for PSV so far.
Still, Madueke will now follow Mykhailo Mudryk and Joao Felix through the door at Chelsea and takes the number of arrivals this month up to six.
The move to Stamford Bridge sees Madueke return home. Born in London, he started his career with Crystal Palace before joining Tottenham and later moved to the Netherlands to continue his development.
PSV have also sold Cody Gakpo to Liverpool this month but van Nistelrooy says the money on offer for Madueke was simply too good to turn down.
“[I have] a mix of emotions,” the former Manchester United striker told reporters.
“We lose a good player because of his departure. There was no turning back and there was a solid financial compensation. I can empathise with the interests of the club.”