The 36-year-old Ronaldo is under contract with Juventus through next June, but Spanish media has speculated about a return to Madrid, where he thrived from 2009-18.
Benzema led Madrid in its Spanish league opener on Saturday by scoring twice in the team's comfortable 4-1 win at Alavés.
It will go down as a slightly controversial appointment given Benitez's close ties with Liverpool, which he managed from 2004-10 and led to the Champions League title in 2005.
Italian Ancelotti, who managed Real Madrid for two years between 2013 and 2015, will sign his new deal on Wednesday, the club said in a statement.
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Bayern Munich scored eight times without reply in their two games since Heynckes replaced Ancelotti a fortnight ago.
Jerome Boateng has revealed how he considered quitting Bayern Munich before Carlo Ancelotti was sacked last month.
Jupp Heynckes on Monday stepped into the position vacated by Carlo Ancelotti, said his advanced age would be no obstacle.
Bayern Munich gaffer Carlo Ancelotti is fully aware of the midfielder Marco Verratti's importance in the French capital.