Ralston, 24, came through the youth ranks at Celtic and has so far played in 60 league games for the Scottish giants.
He has seen his progress rewarded with a new contract which will keep him at Celtic Park until 2027.
Rodgers feels that Ralston took big strides during the period when Postecoglou was in charge at Celtic, following up on his initial promise.
The Northern Irish tactician admitted that Ralston being handed a new contract is something which has left him delighted.
“I am absolutely delighted for Anthony.
“He was a young player who showed a lot of promise when I was first here”, Rodgers told Celtic’s in-house media.
“He came into the team and played some good games, and obviously he really kicked on when Ange came in and had that early spell where he played quite a lot, and you could see him grow from that.
“So, for me and the squad, I’m absolutely delighted.
“He is a Celtic guy who’s come through the system here and I just think that when you have guys like that in your squad, you always get that extra wee bit out of them.
“When I spoke to him a little while back, he is so happy to commit himself to Celtic.”
Ralston has made four substitute appearances for Celtic in the Scottish Premiership this season.
Now with a new contract behind him, Ralston will be looking to kick on at Celtic.