Shane Bauer and Josh Fattal were sentenced in Tehran on Saturday to three years for illegally entering Iran and five years for spying.
The men deny the charges, saying only they may have accidentally entered Iran while hiking in Iraq in July 2009.
Their lawyer has said they intend to appeal against the verdict.
"We have 20 days to appeal and I will try my best to use all legal means to annul the sentence," said Masoud Shafiee.
"It was my belief, and still is, that they are innocent and I have not seen any evidence that shows they are guilty."
Mr Bauer's fiancee Sarah Shourd, who was arrested along with the two men, was freed on $500,000 (£314,386) bail last year.
In a statement on Sunday, Mrs Clinton said she joined President Barack Obama "and the people of the United States in expressing our unflagging support for Shane, Joshua, Sarah and their families during this difficult time".
She added: "We continue to call and work for their immediate release - it is time for them to return home and be reunited with their families."
Mr Shafiee told Reuters he had not seen his clients since their sentencing, but that the two years already served in custody would count as part of their eight-year term.
The men were informed of the sentence on Sunday, he said, after a trial which began in February 2011 and ended on 31 July, the second anniversary of their arrest.
Ms Shourd was released on humanitarian and medical grounds in September 2010 and flew back to the US. She did not return to face trial, saying in May she had suffered from post-traumatic stress and would find a return "too traumatic".
Tehran Prosecutor-General Abbas Jafari Dolatabadi said no verdict had yet been reached in her case, Reuters reports.Rural arrest
Mr Bauer, a freelance journalist and fluent Arabic speaker, had moved in 2008 to the Syrian capital Damascus, where he lived with Ms Shourd, 32, a teacher, writer and women's rights activist. The two met while organising demonstrations against the US-led invasion of Iraq.
Mr Fattal, an environmentalist and teacher, had travelled to Damascus in 2009 to visit his friends.
The trio - all graduates of the University of California, Berkeley - had travelled to Iraqi Kurdistan for a week's holiday. They had visited the tourist village of Ahmed Awa, and hiked along a trail local residents had recommended, Ms Shourd said.
While out walking they were stopped and arrested by Iranian troops who told them they were in Iranian territory. The friends have always maintained that if they did stray into Iran, they did so mistakenly.
The case has heightened the already strained tensions between Tehran and the US.