While the Honduras international is expected to be the second-choice left-back behind Kieran Tierney, Izaguirre has insisted that he is "happy to be home".
"I am happy to be back home," the defender said. "I was seven years at Celtic and I have only the love for Celtic in my heart, so I am happy to be back home. It was a blessing to sign a new contract and I would like to say thank you to Brendan the gaffer, Peter [Lawwell, chief executive] and all the staff at Celtic.
"I am very happy to be back home. I am very happy for [Tierney], he is my boy. I always tried to help him. I am very happy he has progressed.
"I saw him in the youths, he wanted to be a big player and he needs to continue to work hard and try to do the same things he did last year and he can be the best left-back in the world."
Celtic's next fixture is the second leg of their Champions League qualification clash with AEK Athens on Thursday.