Surprising as it may sound, it looks like the School provided it. In Harry Potter and the Philosopher's Stone, Wood suggests a Nimbus as a possible choice for Harry to McGonagall, and she agrees, saying that she needs to go talk to the headmaster to see if an exception can be made.
As far as I know, there is nothing else said about who paid for it specifically, but it sounds like she arranged it through the school. Look at what was in the note attached to it when Harry got it:
DO NOT OPEN THE PARCEL AT THE TABLE.
It contains your new Nimbus Two Thousand, but I don't want everyone knowing you've got a broomstick or they'll all want one.
That could refer to the simple overriding of the First Years can't have them rule... But, given how much McGonagall grumbled about losing the Quidditch Cup before, I think she arranged it, either on her own, or as part of the normal process of getting a 'Replacement' broom for a worn out one. Of the two, I think getting the school (i.e., Dumbledore) to arrange it is most likely, given her personality.
The Harry Potter wiki says that she arranged it (on her page):
Harry made the team, remarkable for a First year, and became the youngest Seeker in a century. McGonagall made arrangements for Harry to have a Nimbus 2000, the fastest broomstick of the time, for use during games and practice
I don't see any source for their statement, tho. It does look like a possible bit of sloppy plotting, honestly -- but it was the first book, with no guarantee more would be desired, so it's not that surprising.
On the other hand, they surely have a budget for outfitting the teams; it's possible she just blew the budget for the next year or so on what she considered a good investment, when she got it for him.
Anyone out there have any quotes from JKR on it? I haven't found any yet..