Remove one nipple from old wheel. Measure down from the bead to where the spoke nipple rests against the hole. In other words, measure from the "outside diameter" to the point where the "spoking diameter" is measured just on one side of the rim. This distance will be around 10-30mm. Now do the same with the new rim. If they are within 2mm of each other, tape the rims together with the valve holes aligned and transfer the spokes one by one to the new rim. Remove the old rim and bring the new one up to tension 1 nipple turn at a time.

If the difference is much more than 2mm, you probably are going to need new spokes.