"We have found an agreement, we have defined the last details which were not important. Tomorrow we will say when Rafael Benitez will be presented," Moratti told reporters on Tuesday.
"We just need a second signature and it is done," he said, without giving further details.
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The Spaniard, who left Liverpool after six years on Thursday following a disappointing campaign, will have the difficult task of matching last season's stunning treble of Champions League, Serie A and Italian Cup success under Mourinho.
Real appointed Mourinho as their new coach last month after agreeing a compensation deal with Inter.
Inter have acted quickly to tie up Benitez, who won the Champions League with Liverpool in 2005 and reached the final two years later having previously also had success with Valencia.
Moratti first targeted England boss Fabio Capello but when the Italian decided to stay until Euro 2012, attention turned to Benitez when he left Liverpool.
Benitez's departure from Anfield came as little surprise after they finished seventh in the Premier League in the season just ended, their lowest position since 1999.
Their failure to advance from the group stages of the Champions League last season and their failure to even qualify for the Champions League next season were ultimately two failures too many for the Liverpool board to accept.
