The 50-year-old Portuguese coach said he is on his way to London to close out the formalities of a return to Stamford Bridge after his exit from Real Madrid was confirmed. Mourinho managed Chelsea between 2004 and 2007, leading the west London club to successive Premier League titles in 2005 and 2006.
"If you have a look at every club Jose has been to, he has always been successful," Harris told Press Association Sport.
Interim manager Rafael Benitez replaced European Cup winning coach Roberto Di Matteo in November 2012, and following some initial difficulties went on to guide the Blues to a third-place finish as well as winning the Europa League.
Harris - who made more than 600 appearances for Chelsea between 1961 and 1980, when the tough-tackling defender was part of the side which lifted the 1970 FA Cup and the European Cup Winners' Cup the following season - is in no doubt Mourinho can push the club back into contention for a first Premier League title since 2010.
Harris added: "People will say he has not done that well at Real Madrid, but he took an unfashionable club like Porto to winning the Champions League, and did the same thing at Inter Milan.
"If he was to come back to Chelsea again, and with one or two adjustments to the squad they will be a major force, challenging for all the major honours again next season.
"If you look defensively, they are quite sound, maybe they will be bringing in another full-back, then a midfield player and another striker or wide player, that would give Chelsea an awesome squad of players."