Brook earned the title shot, which should take place in Las Vegas, when he demolished Hector Saldivia inside three rounds in Sheffield in October.
Alexander won his belt the same night as Brook’s eliminator victory by defeating Randall Bailey and will make his first defence against ‘Special K’
Brook has only fought once before outside of the United Kingdom – a fifth-round TKO of Puerto Rico’s Luis Galarza in Atlantic City on October 8th, 2011 – but is not daunted by having to head Stateside again for his big opportunity.
"I've dreamt of this since I was nine; nothing's going to stop me," Brook said.
"Fighting for the belt in America is going to make it a lot more special.
"I could have had it my own way, in Sheffield for example, but to be honest I don't think he would have come over here.
“I've agreed to fight him in his own country. It's all going to be nice fun and games for me when I get in there and do what I'm going to do - take him out."
Carson Jones, the American boxer whom Brook outpointed in a gutsy performance in July, believes the Sheffield boxer showed enough grit against him to overcome Alexander.
“I am pulling for Brook, hopefully he wins. I think he will stop Devon,” Jones, whose fight with Lee Purdy in England on Saturday was cancelled due to the Englishman suffering a late virus, said.
Champion Alexander said of the defence: “The fight with Brook is definite, we just have to get a venue.
“There has been no time have I thought about vacating my belt as I worked too hard to get it - so I'm definitely going to fight for it.
“As of right now, the fight is on for January 19 and all they have to do is line them up and I’ll knock them down.”