Take My Documents\My Music\iTunes\Mobile Applications from one computer, copy it to the other one over the network, through an external drive. Put it in the iTunes directory on the other computer. Drag the Mobile Applications folder into iTunes, done. Or you could just connect the iPhone to the new computer and under the File menu, select Transfer Purchases if the iPhone doesn't auto-sync or click the Transfer Purchases option that comes up when iTunes recognizes it hasn't synced with this empty library before.