Yes, it's legal.
The thing to remember is you're not replacing lost pieces. You're literally promoting the pawn. It's still the pawn (kind of) but it can move like any other piece you want (other than a king).
So you can also have 2 queens (up to 9!) Bishops of the same color, etc.
can you promote to a pawn?
Well, that would be a nonpromotion. But no, you can't nonpromote. Once the pawn reaches the 8th rank, promotion is mandatory, not optional.
yes, why did you think that you can't?
Law of chess (Fide)
3.7.e
When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival.
This is called the square of ‘promotion’. The player's choice is not restricted to pieces that have been captured previously. This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate.
Yes you can't change the place of promotion. So if your pawn arrives on a8, the only avaible bishop is white, regardless of the color of your remaining bishop (if any), because a8 is a white square. If you arrive on b8, your new bishop has to be black, even if you already have a black bishop and no white bishop, because the square is black.
In a sense, the only way to choose the color of a bishop from promotion is to move a different pawn to the last rank.
this question just came up in our club. thank you for th info. two bishops can be on the same color.
Yes, I once heard there's a problem by Smyslov based on this, unfortunately I can't find it.
In a sense, the only way to choose the color of a bishop from promotion is to move a different pawn to the last rank.
Or the same pawn to a different promotion square. Because a pawn may have a choice between moving and capturing.
More the question is there a position where promoting to a bishop is the best move? This one from a 960 game was unnecessary but it looked cool to have 3 bishops for a move.
this was an interesting thought on promotion.....didn't occur to think about the color of the square
Not a problem:
yes, why did you think that you can't?
Even though I know that you can promote to the same-color bishop, it still somehow feels wrong! 
On one side you finally can stack your bishops attacks on the same square/line (which any other piece could do all along even pawns), but on the other hand half the board is like a parallel universe to both (same-color) bishops - completely untouchable 
As you can see in this game there are 2 bishops and both are on white squares . Here is how it happened . There are only 7 pawns on the board including the one in her hand. The 8th pawn that started off on f7 is the pawn that was promoted . It captured a pawn g6 to be on the g file .The pawn you see on f6 was on e7 then captured a pawn that was on f6. The pawn you see on e5 got there by taking the rook you no longer see on the board . The pawn in her hand started off on 7 that's why she is looking in that direction . So now that the soon to be promoted pawn is on g6 it moved down the board g3 where it captured the pawn on h2 that is no longer on the board . That's how it ended up on the the h file . At the time the rook was in another location . The pawn moved down and was prompted to the white bishop you now see on f7 . As the 2nd white bishop it moved to g2 then f1 then shot up to c4 and to where you see it now on f7 .
C'est assez perturbant mais oui c'est possible
Sometimes you just let your opponents pawns go wherever they want to go and the promoted piece to go where ever it wants to go to make the game last as long as you can . I see no reason to rush but 2 reasons to play as long a possible .
this came up in a forum conversation, and I simply don't know the answer. Say I have a light square bishop and I promote a pawn on a light square. Can I promote to a bishop and have two light square bishops? I realize that I could just as easily promote to a queen, and not face this dilemma, but I guess there could be a situation where promoting to Q could produce an immediate stalemate draw, where promoting to bishop would not. Is it legal to have two bishops of same color, one which was attained by pawn promotion?
Some people may laugh at my question, but you're not born knowing these answers, and you have to learn them somewhere. I looked it up on google search and have not found the answer there.