Since your partitions are showing up as /dev/sda*, that means you're using them directly. A physical partition is inherently part of a single disk, so you can't do it directly.
However, it is possible to create a logical partition that spans multiple physical drives, using LVM. LVM can be set up using the Ubuntu installer, but since you already have a working installation you would need to set it up manually. If you have a separate /home partition, this isn't too difficult:
- From a live CD, back up your
/home partition (e.g. using dd or partimage) to somewhere else.
- Format the old
/home partition and /dev/sdb1 as LVM physical volumes. If you want more space for the root as well, delete the /home partition and recreate it smaller.
- Add the two physical volumes to an LVM volume group.
- Create a new LVM volume using all available space.
- Restore your image onto the new volume. Expand the partition to fill the entire space using
resize2fs.
- Adjust your fstab to tell it to automatically mount your logical partition.
Beware: You will lose the logical partition if either disk fails. Keep good backups.