The updated version will be released on November 15 in the US and November 18 in Europe, one week after the PC port hits the shelves.
The Complete Edition contains all of the game's previously released DLC, as well as the Badge Pursuit Challenge and all additional weapons and outfits.
The PC version features the same bonus content, and offers higher resolution visuals and NVIDIA 3D Vision support.
L.A. Noire was released on Xbox 360 and PlayStation in April, becoming the fastest-selling new property ever in the UK.
Despite the game's success, L.A. Noire studio Team Bondi has begun the process of fully shutting down.
> Read Digital Spy's Xbox 360 review of L.A. Noire
Watch the launch trailer for L.A. Noire below: