He had two spells back on loan at Ninian Park, and is relishing being part of the Bluebirds squad that opens the season in their new stadium next month.
"The new stadium looks magnificent and the lads can't wait for the opener against Scunthorpe," he said.
"These are exciting times for Cardiff and I'm really glad to now be a part of this.
"I'm really glad it's all sorted now and, like all the other lads, I'm excited and determined to go that extra mile to gain promotion."
Chopra follows Anthony Gerrard, who was a target for the Iron, and Mark Hudson in signing for Cardiff this week.
Jeremy Peace, the West Bromwich Albion chairman, has said the club have no need to sell captain Jonathan Greening.
The midfielder has been linked with a return to the top flight, but appears happy to stay at the Hawthorns.
"We can afford to buy before we sell, but we won't sell our crown jewels," said Peace.
"There is a lot of stuff swirling around about Jonno at the moment, but we won't be doing business with our best players."