A former U.S. Secret Service agent was sentenced to nearly six years in prison and agreed to pay $1.1 million for stealing thousands of bitcoin during an investigation into the now-shuttered website Silk Road.

Shaun W. Bridges, who had pleaded guilty to felony charges of money laundering and obstruction of justice, was also sentenced Monday in San Francisco federal court to three years of supervised release after he completes his prison term.

Under...