You must migrate your Kyogre to your Pokemon Black Version. This is done by defeating the Pokemon League the first time and then going to White Forest by going East of Nimbasa City. You will find a route here. Go through it and into the "building" where the guards (which are now gone) were. Cross Marvelous Bridge, and get to the next Route. You will find an important looking building. Inside, you will find a man standing in front of a TV hanging on the wall. If you speak to the man, he will tell you about migrating and how you need 2 DS' to do it. Once you have got onto the little minigame (after following the man's steps), throw a Pokeball at Kyogre. This is a little tricky to do, so time when it appears and get it directly. It does not matter in you do not get the other five Pokemon. If you have hit Kyogre when time runs out, it is added to the PC Box along with any other caught Pokemon. The others will return to HeartGold.
Pick up your Kyogre from the PC and there you have your Kyogre!
PS. When choosing Pokemon from HeartGold's PC, make sure Kyogre is in the PC - it can't be migrated when in HeartGold's party.