Washington did not disclose the terms of the contract.
Hopkins, 27, has spent the past three seasons with the Redskins but missed eight games in 2017 because of a hip injury. He was activated off injured reserve for the final three weeks.
For the season he made 14 of 17 field goal attempts and all but one of his 19 extra point attempts.
Hopkins ranks 24th in field goal percentage over the past three seasons. He also had the ninth-most touchbacks during that period.
His best season was in 2015, when he made 25 of 28 field goal attempts and 39 of 40 extra points.
ESPN's John Keim contributed to this report.