Honduras international Izaguirre, part of his country’s squad for the World Cup next month, has made over 150 appearances since joining the club in 2010. Lustig, who signed in 2012, has made 71 appearances for Celtic, scoring five goals.
The club confirmed the re-signing of the duo on their official website this morning.
Lustig said: “I am absolutely delighted to sign this new contract with the Club. Ever since I came to Celtic I have felt welcomed and I have enjoyed every minute of my time here.
“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.”
Izaguirre said: “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.”