Begiristain recently announced his plan to step down, with Sporting Lisbon's Hugo Viana agreeing to replace Guardiola's trusted advisor.
The Spaniard joined City in 2012 after working in the same director of football role at Barcelona between 2003 and 2010.
Begiristain was widely credited with convincing his former Barcelona team-mate Guardiola to become City manager in 2016.
"Part of me is leaving, I would say. He is a friend of mine and one of the architects of one of the best teams ever from Barcelona, and now here," Guardiola said on Friday.
"I knew the decision for a long time, for family and personal reasons, and I know how grateful he is for this experience here.
"Personally he will be missed a lot. He helped me a lot in my period in Barcelona and of course here.
"But I have the opinion the club is so solid, incredibly well-structured. It has to be like that. All families have to move on and the club will move on."
Begiristain gave Guardiola his first managerial job at Barcelona - the pair struck up a close friendship when they played for the club in the 1990s.
City have enjoyed a golden era with Guardiola and Begiristain calling the shots.
They have won six Premier League titles, including the last four in a row, and the club's first Champions League crown among a host of other trophies.
Begiristain's impending exit will raise further questions about Guardiola's future, with his contract expiring at the end of this season.
The 53-year-old has yet to agree an extension after hinting last season that he could be near the end of his time in England.
There have been reports that Viana would bring highly-rated Sporting boss Ruben Amorim with him to City if Guardiola decides to walk away.
But the Spaniard once again refused to be drawn on his future plans.
"I have to decide. I don't want to talk about it. I've said that many times, and hopefully all of you won't ask me anymore," he said.
