NORFOLK, Va.—Mitt Romney picked Rep. Paul Ryan as his running mate, a decision that could spark enthusiasm for the Republican ticket among conservatives and all but ensures the election will turn to deep philosophical divisions between the two parties over spending, taxes and entitlements.

In Mr. Ryan, 42 years old, the Romney campaign gets a conservative who has spent recent years at the center of national debates about the size and scope of the federal government. With his proposals to revamp entitlement programs for future...