Given that, despite his infidelity, Tiger's never struck me as a complete and total jacka$$, my guess as to the reasons for the agreement would be:
1) Tiger truly wants to attempt to atone for his actions, and this is one way he sees to do so
2) Tiger's legal and PR teams want him to appear to the public to be wanting to atone for his actions
3) As Tiger's an athlete, his ex will likely be spending a significant amount of time raising their children; thus, he wants to appropriately provide for their care and support
4) Tiger plays a sport in which competitors typically compete, at some level, into their 50's and 60's; thus, he has decades of earning potential remaining, so he has the possibility to recoup most, if not all, of this sum
5) Tiger wants to put this entire debacle behind him, and does not want it rehashed two or three years from now with the release of a tell-all memoir from his ex-wife