Benitez, who left Liverpool last Thursday after six years at the English club, will be introduced in Milan next Tuesday after agreeing on a contract with Inter until June 30, 2012.
Mourinho left Inter to join Real Madrid last month after guiding the San Siro club to the Champions League, Serie A and Italian Cup titles this year.
Having started well at Liverpool by winning the 2005 Champions League and 2006 FA Cup, Benitez came under increasing pressure as the club failed to break its run without winning the domestic championship.
Liverpool last won the title in 1990 and in recent years has seen rival Manchester United equal its English record of 18 championships.
Benitez also clashed with American owners Tom Hicks and George Gillett Jr. over a perceived lack of transfer funds. Having led Liverpool to second place in the league in 2009, he saw his team finish in seventh position in the table last season, spelling the end of his tenure.
Before joining Liverpool, Benitez won two Spanish titles and the 2004 UEFA Cup with Valencia.