Booth had been in charge of Ospreys since 2020 and was due to leave at the end of the season.
During his tenure he guided them to the URC Welsh Shield in 2021-22 and 2023-24. He also led Ospreys to the Challenge Cup quarter-finals and the URC play-offs last season.
“It is never nice when a coach leaves his job like that and it is not for me to comment on any decision,” said Peel.
“I just know he has done a good job there.”
Ospreys said in September that Booth would be succeeded by former Wales wing Mark Jones, who has stepped up from his defence coach role to take over six months earlier than expected.
Jones is somebody Peel knows well, the pair having come through the Llanelli youth ranks together into the Scarlets side before also becoming Wales team-mates.
“What he will bring is energy and enthusiasm and will get them emotionally ready for this game,” said Peel.
“Knowing him as well as I have over the last 30 years he will definitely bring those elements to their team and I wish him all the best in the role.
“He is a rugby man through and through and I am sure he will do a good job there.”
