Nokia Corp. and Apple Inc. agreed to bury the hatchet in a long-running legal row, with some estimating Apple will likely pay the struggling Finnish handset maker hundreds of millions of dollars to settle all patent litigation between the two companies.

Apple will make a one-time payment to Nokia and pay continuing royalties as part of a patent-license agreement, Nokia said Tuesday. Nokia—which warned several weeks ago that it might not book a profit in its core cellphone business this quarter in a market increasingly dominated...