The fee, while undisclosed, is believed to be £2.5m, while the Dutch club also announced the signing of Florian Jozefzoon from RKC Waalwijk.
"They are talented players with all the necessary experience," technical director Marcel Brands told the Daily Mail. "Jeffrey is 21 years, Florian 22 years.
"They fit the philosophy that PSV have; we like the best Dutch talent in our ranks."
Bruma made nine appearances during his time at Chelsea.