The thoroughly hair-gelled image debuted at Entertainment Weekly as part of their fall preview issue.
For comparison, here's a look at a younger Hoover:
UPDATE: EW has posted three more photos from the film, giving our first look at Armie Hammer and a shot of Eastwood directing.
Interestingly, J. Edgar Hoover was recently played at an overlapping time period by Billy Crudup in Michael Mann's Public Enemies.
This particular biopic has a rather classy pedigree, with DiCaprio and four time Academy Award winner Clint Eastwood, along with Dustin Lance Black, who won an Oscar on account of his excellent Milk screenplay.
The story will apparently incorporate much of Hoover's private life, including his secret relationship with Clyde Toulson, played by Armie Hammer. Also on board are Naomi Watts, Josh Lucas, Dermot Mulroney, Judi Dench, Ed Westwick, and Stephen Root.
J. Edgar is set for release on November 9th, right in the midst of the prestige season.
And because it's so, so good, and I'll take any excuse I can, here's a clip from The Aviator: