The clubs agreed a deal on Friday, reported to be a club-record fee of roughly £7million, although Hull have not confirmed whether it is a record-breaking deal.
Hull have impressed on their return to the Premier League and sit 10th after 20 games, but they have been far from prolific.
With a total of 22 goals - including six put past Fulham in one game - Hull's top scorer in the league is Robbie Brady with three to his name, all of which came within the first six games of the campaign.
Jelavic commented of the switch: "I realised straight away that manager was really interested in signing me and that it is a great opportunity for me to come here.
"It is a good club, and we have a good squad. We talked a little bit, but it didn’t take long to realise that it was right for me.
"It's a newly promoted club, but I can see straight away that there is a lot of ambition here within the club.
"I hope that we can build on the great start to the season and become a really strong Premier League team over the coming years."
A striker has been high on Bruce's list of priorities, with a long-term pursuit of Shane Long being routinely rebuffed by West Brom.
