He began his career as a trainee at Everton, and won England Under-21 honours.
After only getting three goals for the Toffeemen, he went to Wolvehampton Wanderers in a £500,000 deal in January 2000.
But in two seasons there the 23-year-old has only found the net 6 times in over 50 starts, leaving him surplus to requirements.
Branch said: "The talks between my agent and Hull City had been ongoing for the past couple of weeks and he rang me on Thursday night to say that the deal had been done.
"I need to be playing football and I'm not doing that at Wolves. When Dave Jones came in as the manager he brought some new players along and I don't figure in his plans at the minute.
"There were one or two other clubs who were interested in taking me on loan but I had a chat with Phil Jevons and Carl Regan, both of whom I know, and they convinced me that coming to Hull was the right move.
"From a personal point of view I just want to be playing games. I'm here for a month initially and we'll take things from there."