"Bye bye Nadine … What a long strange trip it's been," the National Hurricane Center in Miami said in its final advisory for Nadine.
The remnants of the storm could produce gale-force winds in the Azores over the next 12 hours, with an additional inch of rainfall.
Tropical Storm Oscar, with maximum sustained winds of 45 mph, was about 1,170 miles west-northwest of the Cape Verde Islands, moving north-northwest at 12 mph, the hurricane center said in its 5 p.m. advisory.
No coastal watches or warnings were in effect.
Oscar was forecast to accelerate northeast during the next day or so.
Little change in strength was expected before Oscar dissipates in 24 to 36 hours.
Tropical storm-force winds extended up to 205 miles from the center.