Which version of iPhoto did you have on your old Mac? On your new Mac with Yosemite you need iPhoto 9.6.1. This version is only available from the AppStore. But apple stopped selling iPhoto from the App Store.
You can no longer buy iPhoto from the App Store anywhere, and also not update it from the "Updates" tab of the App Store. You can however reinstall it, if it is showing among your Purchases at the App Store and associated with your AppleID. It is unlikely, that you have been using an iPhoto version on Snow Leopard, that has been sold from the appStore or associated with your appleID at the AppStore.
Sign into the App Store and look at the Purchases tab. Is iPhoto listed there? Only if you see it there, can you reinstall as described in this User Tip:
Get iPhoto 9.6.1 if you didn't update before OS... | Apple Support Communities
The main idea is to move the incompatible iPhoto app to the Trash, so Spotlight does not see it as installed, reload the App Store by pressing ⌘R, and then to try to download again from the App Store - from your Purchases tab, not from the main page, since you can neither buy iPhoto nor update it, but you can reinstall, if your AppleID is associated with it.
So move iPhoto to the Trash (don't empty the Trash), relaunch the App Store. The button to the right if iPhoto should change to Install on the "Purchases" tab.
If you do not see iPhoto there, try to unhide your Purchases as described on this page: Hide and unhide purchases in the Mac App Store - Apple Support
If you do not own an AppStore version of iPhoto you will not be able to install iPhoto on your new Mac, unless you can talk the App Store Support into providing you with a redeem code for iPhoto so you can install it.
Otherwise you can try to open your iPhoto Library in the new Photos.app that came with your new Mac as part of Yosemite.
