As long as they use the same interface, yes. Laptop/desktop vendors use hard drives from the same set of vendors (Seagate, Hitachi, WD, etc) which use interchangeable standard connectors. Older drives used the IDE/PATA standard while newer drives use SATA.
You'll have to re-install windows since the drivers installed on the HP laptop won't match the hardware in a different model from Toshiba.