Jones, 33, penned a one-year deal with the Bantams ahead of training on Monday morning to become City's tenth new signing since the end of last season.
The Australian goalkeeper will now battle it out with City's current custodian Ben Williams for the club's number one spot.
Jones isn't expected to start in this Tuesday's home league fixture with Gillingham although he could be named among City's substitutes for the game.
Parkinson said: "I'm absolutely ecstatic with the signing of Brad.
"Patience and perseverance has finally paid off for us. Out of all the goalkeepers we have looked at over the summer and all the goalkeepers who were available, Brad Jones was always the top one we really wanted.
"Did I honestly believe we could get him here? I think we knew it was always going to be tough but we stuck in there. Right up until Saturday, we were competing with other clubs for his signature.
"He comes to us with not a great deal of training under his belt so he is going to take some time to get up to full speed. In the long run though, he will be a great acquisition for us.
"Brad will now give us great competition for that 'keeping spot.
"Ben (Williams) has come back this season in great shape but everybody wants two senior players for that goalkeeper position.
"When you look at the loan market, as we did last year, the only problem with that is you are normally under pressure to play him (the loan goalkeeper). That goalkeeper has to be really, really good to justify being number one week in, week out.
"Any loan 'keeper we would have brought in this season would have needed to be a really special player to merit keeping Ben out of the team all of the time.
"Now we have signed our own goalkeeper in Brad, however, we can have genuine competition between the both of them and the best one out of those two will play."