The deal values the company at almost 1.7 billion euros (1.46 billion pounds), including debt, or at about 13 times its expected 2021 core earnings, three people close to the matter said.
Permira and the seller, private equity firm Apax, declined to comment on the financial details of the deal.
The British buyout firm prevailed against competing offers from Carlyle, ICG and Goldman Sach's private equity arm, the sources said.
The runners-up also declined to comment.
Apax bought Neuraxpharm in 2016, combined it with Invent Farma, and later strengthened the company through add-on acquisitions, such as FB Health and Farmax.
The company makes specialty pharmaceuticals for neurological and psychiatric disorders, including epilepsy, Parkinson's disease, Alzheimer's disease, depression and psychosis. It has annual revenues of more than 460 million euros and 850 employees.
While global M&A activity hit its lowest level in more than a decade in the second quarter, deal-making in the healthcare sector is expected to buck the trend this year as its products and services are considered resilient to the COVID-19 crisis, investment bankers say.
Jefferies advised Apax on the deal, which Reuters flagged in July, while Rothschild advised Permira.
Jefferies is supplying a pre-arranged financing package - so-called staple financing - of more than 6.5 times core earnings, a source close to the matter said.
Apax Global Alpha, which is an investor in the Apax VIII fund selling Neuraxpharm, said the deal is expected to result in a gross multiple on invested capital of 3.5 times and a gross internal rate of return of 36%.
($1 = 0.8517 euros)
By Arno Schuetze