Maxwell, 27, batted .144 with three home runs and 12 RBIs in 67 games for Washington last season. He also played in 66 games at Triple-A Syracuse, batting .287 with six home runs and 21 RBIs.
"I'm very excited," Maxwell said. "I feel blessed that the Yankees were willing to take a chance on me considering I'm coming off offseason surgery. I'm excited for the new opportunity and for the new year."
Maxwell had Tommy John surgery on his left (non-throwing) elbow in October after attempting a diving catch in the second-to-last game of the season against the Mets. He believes the surgery will not present an issue this spring.
"We're a little over three months out and I feel pretty much 100 percent," Maxwell said. "I've already been hitting and throwing, doing everything. I feel good."
Maxwell was designated for assignment by the Nationals on Thursday. He has a career batting average of .201, with nine home runs and 26 RBIs in 122 Major League games over parts of three seasons.
The Yankees figure to use Maxwell as outfield depth in a group that includes Colin Curtis and Greg Golson, both of whom spent time at the big league level last year.
If he does not make the team out of camp, Maxwell has one Minor League option remaining; the Nationals filed for a fourth option after the season and were awarded it.
"I'm just going in there for anywhere I can to help the team," Maxwell said. "If they're thinking more outfield depth to give the team some options, I'm just happy they're willing to take a chance on me considering my circumstance. I'm looking forward to starting the season."
Olbrychowski, 24, was a fifth-round selection of the Yankees in the 2007 Free-Year Player Draft. Olbrychowski pitched most of last season at Class A Tampa, going 3-2 with a 4.02 ERA in 30 games (one start).
He also made two relief appearances at Double-A Trenton, where he had no record and a 2.08 ERA. In four Minor League seasons, Olbrychowski is 16-17 with a 4.17 ERA over 100 games (35 starts).
In order to create room for Maxwell on its 40-man roster, New York designated outfielder Jordan Parraz for assignment. Parraz was claimed off waivers by the Yankees from the Red Sox on Dec. 17.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.