Joshua won the IBF heavyweight world title in April with a knockout victory over American Charles Martin and then successfully defended his belt with the stoppage of the previously unbeaten Dominic Breazeale in June.
And now he faces Molina, who has 19 stoppages in 25 wins and just three defeats. The 34-year-old Texan stretched WBC champion Wilder to the ninth round before being stopped in June last year.
"I am pleased that everything is now set for December 10 and I can concentrate on getting the business done in the ring," said Joshua. "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 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."
Molina is confident of causing an upset in Manchester and said: "There is no heavyweight in the world that has bounced back like I have. That's the man that Joshua faces on December 10 and that man is a very dangerous one.
"He'll fight the toughest Molina that anybody has ever seen, just like Adamek fought the toughest Molina.
"'I'm confident. These type of fights don't shake me up, I'm a very strong mental fighter. I know exactly what I've got to do to prepare myself in the amount of time. I know exactly what I've got to do, mentally, physically, to go there and perform.
"When you walk out into the atmosphere, half the battle is the mental battle, and if you can stay in the moment mentally you have a shot in any fight."
Joshua's Promoter Eddie Hearn, said: "The heavyweight division has been turned on its head in the last few months and while many are standing still waiting, I'm delighted to get this huge card up and running in Manchester.
"'I have spoken to Eric Molina at length and I know this is going to be a big test for Anthony. We saw in the Wilder fight that he can punch and doesn't give in and is coming off a strong knockout win against Adamek in his back yard in Poland. We have requested an exception from the IBF for this fight and although the plans are for a major unification in the spring this fight requires Anthony's full focus.
"The card is one of the strongest we have produced, supported by a huge all-British Heavyweight grudge match between Dillian Whyte and Dereck Chisora which will be an official eliminator for the WBC World title."
