Gordon made landfall as a Category 1 hurricane early Monday morning, but Portugal authorities say the storm passed without causing major damage.
Emergency services responded to some calls about localized flooding, but there have been no reports of injuries.
Locals were warned to take precautions ahead of the hurricane, which developed on Saturday.
Gordon has now been downgraded to a post-tropical storm and Portugal has discontinued the hurricane warning for the eastern Azores.
Helene approached Mexico's coast on Saturday as a tropical storm, but quickly weakened into a tropical depression then degenerated into a rain storm.
Officials were worried that Helene's rains could pose a threat to areas where thousands of people were still recovering from flooding spawned by Hurricane Ernesto. So far however, no significant damage has been reported and none of the region's rivers have overflowed.
On Friday, Helene became the 8th-named storm of the 2012 Atlantic Hurricane Season.