Frandsen received a guaranteed $900,000 major-league deal from the Nationals, plus $300,000 in performance bonuses and a $400,000 awards package.
Frandsen is expected to fill a utility infield role for the Nationals and give manager Matt Williams a right-handed bat off the bench.
"It's important for your team to have guys that can move around and that are experienced in that regard and have done it," Williams said before his team's 3-2 loss to the St. Louis Cardinals on Wednesday.
To make room on their 40-man roster for Frandsen, the Nationals voided their previous option of right-hander Ross Ohlendorf and put him on the 60-day disabled list with a right lumbar strain.
Jamey Carroll, who had been considered a top candidate for the utility infield role in Washington, was released by the Nationals on Tuesday.
Information from the Associated Press was used in this report.