The Welshman spoke to the media for the first time since being handed the role on Tuesday.
The club opted to sack Moyes less than 10 months after he was appointed as Sir Alex Ferguson's successor following 15 defeats in all competitions.
"I would like to go on record to thank David Moyes for giving me my first chance in coaching," Giggs told reporters. "It is something I will always remember. He gave me the opportunity for my first coaching role."
Giggs, who confirmed that he will continue being involved as a player, is not expected to continue his role as manager into the new season.