Cardiff will allow long-serving Kevin McNaughton to leave this summer along with Danny Gabbidon and Nicky Maynard.
Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
The 19-year-old, who has made 19 first-team appearances and scored in last season's William Hill Scottish Cup semi-final win over Falkirk, recently returned from a five-month absence following a broken ankle.
Harris told the club's official website: "I'm delighted to have agreed a new contract - Hibs is my home and I'm really pleased that the deal has been agreed.
"My long-term goals are to establish myself in the first team, build on my performances from last season and help to push the team up the league.
"The new manager has already shown a lot of faith in me which is really encouraging and I just want to kick on from here."
Manager Terry Butcher said: "I'm really excited that Alex has put pen to paper and that he will be a Hibernian player for a long while.
"We're delighted to have him back from injury and part of our long-term plans. Alex came off the bench on Saturday and did well - his performance improved as the game went on and that augurs well for the future."