The teenage left-back had been linked with a switch to the Premier League champions and reports had suggested John Guidetti could be included in a swap deal.
Guidetti ruled out any prospect of joining PSV on Tuesday and now Willems has committed his future to the club by agreeing a deal at Philips Stadion until 2017.
"When I came here from Sparta Rotterdam I had not achieved anything," the 19-year-old told the club's official website. "Now I have already played at the European Championship."
Willems joined PSV in 2011 from Sparta and broke into the first team following injuries to fellow defenders Erik Pieters and Abel Tamata.
He was included in the Netherlands' squad for Euro 2012 and he was the youngster player to appear in the tournament in Poland and Ukraine.
The youngster now wants to follow up signing a new contract by helping PSV to win the Eredivisie title, saying: "First we have to win on Sunday against Ajax."
PSV are currently second in the table and trail leaders Ajax by three points ahead of the weekend's crunch clash in Eindhoven.