The English Premier League club didn't disclose a fee but confirmed it would exceed the £15 million ($26.9 million) deal that brought Alan Shearer to St. James' Park in 1996.
"Newcastle have met Real Madrid's asking price and conditions Newcastle said in a statement.
"The agreed fee will be a record transfer fee for Newcastle United. It is now up to the player and his advisor."
Real Madrid also confirmed a deal had been reached that would allow Owen to leave the Spanish giants just one season after arriving from Liverpool.
"Newcastle have made a very serious offer that has met the requirements of Real Madrid the club's Director of Communications Antonio Garcia Ferreras told Reuters.
"The move now depends on Newcastle and the player reaching an agreement themselves but as far as Real Madrid is concerned Michael Owen has the go-ahead to leave."
However the deal still depends on Owen agreeing terms with Newcastle -- and the player said after talks with Real President Florentino Perez on Tuesday that he favored a return to European champions Liverpool.
"The president understood and said he would try to help me achieve this said Owen.
"If the transfer cannot be finalized in time I have agreed to go to Newcastle United but only on a one-year loan. I need to be playing regularly in a World Cup year."
Real paid £8 million ($14.3 million) for the 25-year-old last year but Owen's future in Spain has been in question ever since after he failed to earn a starting place at the club.
Last season Raul and Ronaldo were Real's first choice strikers with Owen contributing 16 goals mainly as a substitute.
The arrival of Brazilian strikers Robinho and Julio Baptista at the Bernabeu means he is likely to face even stiffer competition for playing time if he stays with Real.