Pearce, the England Under-21 manager, was given control of the senior side for the match against the Dutch at Wembley following Fabio Capello's resignation on Wednesday.
Capello quit just four months before the start of Euro 2012 following the FA's decision to strip John Terry of the England captaincy ahead of the Chelsea defender's trial on charges of racially abusing QPR's Anton Ferdinand, which is due to take place after the tournament in Poland and Ukraine.
Former England defender Pearce, who was Capello's assistant, will take charge of the Great Britain's men's Olympic team at the 2012 Games in London.
"I can announce that Stuart Pearce will manage the England team against Holland," said Bernstein at a Wembley news conference on Thursday.
"He has huge experience outside and inside the organisation. He has been working with the under-21 team and has been working with Fabio for some time. I have got great confidence in Stuart, we will be in good hands.
"Our priority then will be to appoint a new England manager."
Tottenham manager Harry Redknapp, cleared of tax evasion charges on Wednesday, remains the overwhelming favourite to succeed Capello on a long-term basis.