The 23-year-old former Aston Villa player only joined the Owls in mid-January, but has never been allowed to move onto pastures new in a bid to revive his career after an underwhelming spell in South Yorkshire.
On Green, who started the club's first two league games of the campaign, Moore said: "We had the interest from the club he has gone to now and like anything else, his representatives and his agent made the club quite aware of the interest from the other club.
"We felt it was right for us as a football club in terms of where Andre was at, in the final year of his contract and everything else. They made the right offer, which is good for the football club.
"We sincerely wish Andre all the best in his next career step and move."
On whether he will be replaced, Moore added: "We have options and people who can play in his role at the football club. Players who the supporters have not seen yet this season.
"We feel we have players who can play in that position and when the time is right, hopefully we can bring those players to play their part for the team."
Moore will make a late decision on the fitness of defender Sam Hutchinson, who has been suffering from general soreness following the hectic demands at the start of the season, on Saturday morning ahead of the League One derby at Rotherham United.
Olamide Shodipo is back in training, but the game comes too soon for the loanee with Josh Windass (hamstring) still out.
Theo Corbeanu is back available ahead of Saturday's game.
"Theo has had a good, solid week's training and we are glad to have him in and around the squad and he will be part of the squad," Moore said.
The Owls chief has no fresh concerns.