Can I upgrade obsolete units, and if so, how?

When you change your default unit type (e.g. because of an upgrade to a better unit), all your troops will automatically "evolve" into that new unit type. There are no further actions you have to do about that. This will happen always when you change a unit type.

Keep in mind however that changing a unit type will give all troops that contain the affected existing units a severe drop in morale. This is due to the short-time chaos that comes with reorganizing a regiment.

For this reason, changing the unit type in the middle of a war can be a bad idea, depending on the situation of course.