There had been hopes that the unbeaten 26-year-old might face Wladimir Klitschko
There had been hopes that the unbeaten Joshua, 26, might face Wladimir Klitschko after the former heavyweight champion's re-match with Tyson Fury, was postponed.
But contractual wrangles and a minor injury suffered by the Ukrainian scuppered the hopes of that bout taking place this year.
Molina, a 34-year-old Texan, has won 25 of his 28 professional contests and took World Boxing Council (WBC) champion Deontay Wilder to the ninth round before being stopped last year.
Joshua, the Olympic super-heavyweight gold medallist from the 2012 London Games and unbeaten in 17 professional fights, said: "I am pleased that everything is now set for December 10 and I can concentrate on getting the business done in the ring.
"There has been plenty of talk about who I may face but all I'm doing is concentrating on finishing Molina in style and putting on a great show.
"Every fight is dangerous in this division and this is no exception. I saw Molina have a great fight with Wilder and he is now coming off a strong KO win against (Tomasz) Adamek in Poland.
"I'm expecting this to be the toughest fight of my career so far and I will be ready for an all-out war."
Joshua last fought when he stopped Dominic Breazeale in seven rounds in June, having overwhelmed Charles Martin to take the title two months earlier.
He will be the firm favourite to hang on to his belt in Manchester but Molina said: "There is no heavyweight in the world who has bounced back like I have.
"That's the man that Joshua faces on December 10 and that man is a very dangerous one.
"I'm confident. These types of fights don't shake me up. I'm a very strong mental fighter. I know exactly what to do, mentally and physically, to go out there and perform."