Brook, 23, claimed the title last June by beating Welshman Barrie Jones and has defended it three times.
Former British champion Jennings, 31, was stopped in five rounds when he challenged Miguel Cotto for the WBO welterweight title in February.
Brook said he took the fight because he has “unfinished business at home”.
The unbeaten Sheffield fighter, who has 13 KOs from his 20 fights, said he could have moved on to European or even world level but wants to beat Jennings “to be number one”.
“Having fought Cotto, he is known in the States, and if I do a job on him I can make a big statement about my abilities at world level,” added Brook.
“I’ve taken out each of my last three opponents in the first three rounds, and I can do something similar against Jennings. He’s a slow starter and I know I can get him out of there quickly.”
“Brook’s a good kid and he’s done well to win a Lonsdale belt outright,” he said.
“But let’s be honest, who has he really fought? It’s not until now that he’s met someone who can stand up to him, and believe me I will do.
“People asked me if I was going to retire after the Cotto fight, but the thought never crossed my mind.
“I want title fights and I’m delighted that I’ve got Brook, because this is an opportunity for me to get back into the big time.
“Everyone is talking about him as the future of British boxing, but I’ll take him to school.”