The Scotland Under-21 international has penned a two-year-deal and his arrival follows on from the capture of Callum Cooke as City step up preparations for next season.
Watt began his youth career at Preston before joining Wolves in 2016, making his senior debut two years later.
The playmaker spent the second half of last season on loan at Carlisle United, where he netted once in 14 appearances.
On joining Bradford, he said: "I am buzzing to be here and cannot wait to get going in pre-season.
"From the minute I heard Bradford City was interested, it was straight ahead. I wanted to get the deal done.
"The size of the club speaks for itself and we should not really be in the division we are. I am here to work hard and help get this club where it deserves to be.”
On bringing in Watt, City boss Stuart McCall - who has also brought in Levi Sutton and Billy Clarke this summer - added: "Elliot is a player I have had my eye on for quite a while, now. I knew of him when he was at Preston as a kid, and then when he went to Wolves.
"He is very hungry and wants to get out and make his mark. He is a really technically-gifted ball player who has international experience at youth level with Scotland.
"Even though he still had another year left on his contract, Wolves were happy to let him get out and play football, and we have high hopes for him."
Watt’s signing is subject to the relevant EFL and FA clearances.