The French Under-21 international had been linked with a move away from Celtic all summer with a number of clubs showing interest in securing his services.
However, the Eagles stole the race in the last few days and confirmed a £14m move for Edouard on a four-year deal.
Parish, while giving his reaction to the signing, revealed that the club were delighted to see the 23-year-old choose Crystal Palace over others; he also hailed Edouard’s quality.
“Odsonne is a player of proven quality”, Parish told his club’s official site.
“He was a player in high demand and I’m delighted he chose to join Crystal Palace as another fantastic addition to our squad.”
Edouard on his part insisted that scoring goals in the Premier League might be the biggest challenge of his career but he is aiming to meet that challenge.
“I’m very happy to be here today. I can’t [wait] start to train with the team and to play for this club.
“Scoring goals in the Premier League may be the biggest challenge in my career.
“But I’m confident in myself and my teammates to be successful.”
In the three seasons Edouard was in Scotland he managed to score an impressive 86 goals, helping set up 39 more for his team-mates.
He was into the final year of his contract at Celtic.