Booth had been in charge of the Ospreys since 2020 and was due to leave at the end of the season.
During his tenure, he led them to the URC Welsh Shield in 2021–22 and 2023–24. He also led the Ospreys to the Challenge Cup quarter-finals and the URC play-offs last season.
“It’s never nice when a coach leaves a job like this and it’s not my place to comment on any decision,” Peel said.
“I just know he did a good job there.”
Ospreys said in September that Booth’s successor would be former Wales winger Mark Jones, who moved from his position as defense coach and took up the post six months earlier than expected.
Jones is someone Peel knows well. The pair, who came through the Llanelli youth ranks, joined the Scarlets team together before also becoming Wales team-mates.
“What he will bring to the team is energy and enthusiasm that will prepare them emotionally for this game,” Peel said.
“Knowing him as well as I have over the last 30 years, he will certainly bring these elements to their team and I wish him all the best in this role.
“He is a rugby player through and through and I am sure he will do a good job there.”
