I am this kind of player. I know it all too well, and more than once my GMs have talked to me about it.
In my case, I "grew up" with DnD power-gamers, the types of players who dedicate themselves to creating the most powerful character possible within the rules, often bending said rules all the way to the breaking point. As a result, that's how I know how to build characters: power-gamer style, sometimes game-breakingly so.
The problem for me is that I'm not a power-gamer -- I'm a role-player. I play for the narrative, not merely1 the dice-rolling with maximum possible bonuses. When I create a character for power-gaming, most often I have no concept of "who this is", and thus fail completely to connect to it from an RP point-of-view -- which leads to me getting bored and scrapping the character.
When my GMs spoke to me and discovered this, they sat down with me and together we figured out a character concept I wanted to play -- one that I could connect with RP-wise -- and then helped me power-game it within that concept (this part was so that I could actually contribute, as any character that wasn't power-gamed in these games was basically just scenery). In most cases this ended my constant character-switching.
The takeaway here for you isn't that your games are for power-gamers and your character-switching player is an RPer. I can't know either of those things. The takeaway is rather that you should sit down and talk to this player and find out why he does this. Maybe he's a power-gamer that feels ill-fitted to your RP-centric game; maybe he's a (non-power-)gamer here for the dice-rolling who gets bored in your RP-centric game; maybe he's an RP gamer who finds himself unable to connect with his power-gamer builds.
The point is that sitting down and talking with him is how you figure out what the problem is. From there, work with him to solve it, up to and including potentially helping him build a character he'll be happy sticking with -- or, if he's just that type of player who constantly likes trying out new things2, maybe it's time to politely suggest he find a group more amenable to that -- or else adapt to it yourself, for instance by crafting a plotline for the group as a whole that explains their high turnover rate, and/or accepting that this player will only have generic plotlines fitting for whatever character he brings with him today, or no plotlines at all (this should be part of your discussion, of course).
1 I don't say this to disparage this play style, just to differentiate my own from it.
2 In other contexts I'm this player, too -- in Skyrim, for instance, I have a dozen characters, only one higher than level 20, because I constantly stop one to try out a different type of character.