Peter Ridsdale said: "We have initially signed Michael on loan.
"And we've agreed with him and Sunderland a permanent deal, which will become effective from July 2.
"Michael signed and his paperwork was lodged with the Football League and Premier League with 55 seconds before the window closed.
"So it was a close call.
"I've spoken to Michael and he is obviously delighted as he was getting frustrated by the lack of opportunity he was getting at Sunderland and has a lot of friends at Cardiff.
"He is over the moon, I'm delighted and Dave is grateful that we've got in the players he wanted during the transfer window."
The permanent deal for Chopra is thought to be worth over £3m in value. It's his third spell at Ninian Park, he scored 5 goals in 10 games on loan before Christmas.