Guardiola penned terms to 2023 last week.
He wrote in today's match programme notes: "This is the first time I have written to you since signing my new contract.
"I am delighted to be here, with so many great people supporting me. Khaldoon, Txiki, Ferran, all my backroom staff, my players and our fans – there were so many reasons for me to stay longer and continue trying to win more trophies for this great football club.
"I have seen many times the support I have received during difficult periods here.
"For a manager, there is nothing more valuable and I appreciate it so much."
Guardiola also said: "There were plenty of positives to take from our win against Olympiakos – and from our Champions League campaign so far. To qualify after four matches is perfect, especially in a season with such a challenging schedule.
"It is the eighth-consecutive season this club has qualified for the last-16 and believe me it is not easy getting to the knock-out stages. You have to play teams who are conditioned to win matches and we should be proud to have made it through after four wins from four so far."