Despite currently being without a manager following Neil Lennon's departure, the club have tied the two defenders down to long-term deals.
Honduras international Izaguirre joined from Motagua in 2010 and has since made 151 appearances for Celtic.
After an impressive debut campaign, Izaguirre has helped Celtic to three league titles in a row, while Lustig is a more recent addition.
Following his signing from Rosenborg in 2012, Lustig suffered a number of recurring injuries but recovered to clinch two league titles and a Scottish Cup crown.
Izaguirre, currently preparing for the FIFA World Cup with Honduras, told the club's official website: "Celtic is a place I have called home for a number of years now and it is the place where I want to be in the future.
"It is a magnificent football club in a great city, somewhere my family have settled so well.
"I would like to thank the Celtic fans for all the support they have given me over these years and I now want to look forward to many more happy and successful times with these supporters."
Lustig added: "It has been brilliant to win trophies here and I hope we can go again next season and bring more silverware to Celtic and achieve one of our main objectives in the next few months and take Celtic to the Champions League again.
"It is, of course, disappointing that Neil has left the club as manager and obviously all the players wish him all the best for the future.
"However, I knew that I wanted to be part of Celtic going forward and I am so pleased that I have been able to commit my future to such a great club."
