Kehrer, a Schalke youth product, initially broke into the club's first-team squad in the 2016-17 campaign before going on to enjoy a breakthrough season last term.
The 21-year-old defender started 27 games in the Bundesliga in 2017-18 as Schalke finished second to Bayern Munich.
Kehrer had agreed to a contract extension at the club, according to Heidel, but PSG then came in with an offer the club could not refuse.
"Without an offer of the dimension that PSG has given us, Thilo would have certainly extended," Heidel told a news conference on Sunday.
#Heidel: "@KehrerThilo will leave Schalke. Rarely have I known such a loyal and well-to-do young man. We had already agreed a contract extension." #s04 pic.twitter.com/X8EhpWqKui — FC Schalke 04 (@s04_en) August 12, 2018
"We have basically agreed on a contract with Paris.
“The transfer will have an economic significance that Schalke 04 can not refuse."
The signing of Kehrer will likely bring PSG's pursuit of Bayern defender Jerome Boateng to an end.
Boateng - a reported target for Man Utd before the Premier League transfer window closed - has been linked with a switch to Parc des Princes to team up with compatriot Thomas Tuchel.