As I wrote here, speculation for quite a while has centered around Geithner and former Treasury Secretary Larry Summers.
If that is indeed what the choice came down to, Obama may have opted for Geithner for two reasons: 1) his reputation has risen, due to his role in dealing with the financial crisis; and 2) Obama may have wanted to avoid questions about the controversial manner in which Summers left the presidency of Harvard.
Stock markets rallied yesterday, after significant losses earlier in the week. Those who write such things have called that Wall Street's endorsement of Geithner.
Presidents, maybe with some reluctance, tend to acknowledge the need to gain acceptance, or at least lack of hostility, on the part of the financial types, to their economic personnel and policy choices.
Again, the wisdom on this point comes from James Carville, that political consultant I would love to ignore, but he's just too quotable. At the beginning of the Clinton Administration, when the president and his staff cited financial market considerations as their rationale for turning their promised tax cut into a tax increase, Carville mused about reincarnation:
I used to think if there was reincarnation, I wanted to come back as the President or the Pope or a .400 baseball hitter, but now I want to come back as the bond market. You can intimidate everybody.