The 55-year-old ex-Liverpool boss ended a two-year stint with Napoli following a 4-2 home defeat by Lazio on Sunday.
“I am enthusiastic and happy, although there are things that still need to be discussed,” Benitez said upon his arrival in Madrid.
Madrid-born Benitez will replace Carlo Ancelotti, who was sacked last week just a year after winning the Champions League against Atletico Madrid.
Real confirmed on their website Benitez would be unveiled at a press conference at 12:00 BST on Wednesday.
Spaniard Benitez will arrive at the Bernabeu with plenty of European pedigree, having won the Champions League with Liverpool in 2005, Uefa Cup with Valencia in 2004 and the Europa League while interim manager at Chelsea two years ago.
Benitez started his coaching career with Real’s youth squad but it was with Valencia that he made his name.
He led them to two La Liga titles before leaving for Liverpool, where he also won the FA Cup and Uefa Super Cup.
After ending a six-year stay at Liverpool he moved on to Inter Milan but was sacked just three months into the 2010-11 season.
He bounced back by leading Chelsea to the Europa League title in the 2012-13 campaign before joining Napoli.
The Spaniard then guided the Italian side to the Coppa Italia in his first season in charge, but the loss to Lazio meant the club finished fifth in Serie A and did not qualify for the Champions League.