The Clint Eastwood directed film will open the 25th edition of the Hollywood, California film festival on November 3.
J. Edgar is scheduled to open nationwide on November 9.
In the film, Hammer, the 25-year-old co-star of last year's The Social Network, plays Clyde Tolson, Hoover's co-worker and lifetime partner.
The film's screenwriter, Dustin Lance Black, who won an Academy Award for penning Milk, has already promised a “tender” kiss between the film's leading men.
“Yes, certainly there's a relationship between these two guys,” Black told E! Online.
“And it wouldn't be a Dustin Lance Black script if it didn't have a little gay kissing in it. So the answer is yes.”
“Those who want to see that will be pleased. I think it's done in a very tender way, surprisingly,” he added.
The film also stars Denis O'Hare (True Blood), Josh Lucas (Glory Road), Ed Westwick (Gossip Girl), Naomi Watts (King Kong) and Judi Dench (Casino Royale), and is directed by legendary actor-director Clint Eastwood.