The team announced the signing Wednesday.
Galette had wanted a one-year deal all along, hoping he can prove that he's not only recovered from the Achilles injury he suffered before last season, but that he remains a solid pass-rusher.
The Redskins controlled his situation all along because Galette had given them the right of first refusal when he signed a one-year deal with them last summer. A strong market did not develop for his services, giving the Redskins a potential premium pass-rusher who will cost, at most, $4 million.
The Redskins have mostly focused on re-signing their players this offseason. Of their nine moves, seven have been to either re-sign one of their own or give an extension.
Galette, who turns 28 on March 27, missed the 2015 season after tearing his Achilles' tendon in practice leading up to the opener.
Washington had signed Galette in August, after New Orleans released him.
Galette was suspended by the NFL for two games without pay in accordance with the personal conduct policy. He served the suspension last season while on injured reserve.
Galette was arrested and faced charges of misdemeanor simple battery/domestic violence in early January 2015 after an incident at his home in Kenner, Louisiana. Following an investigation, the charges were dropped a month later.
The accuser then filed a civil suit against Galette, alleging three years of sexual, physical and mental abuse. But that suit was dismissed in August after the woman failed to pursue the case.
New Orleans released Galette less than a year after signing him to a four-year, $41.5 million contract extension.
Galette spent his first five seasons with the Saints, leading the team with 22 sacks in his last two years combined. He has 31½ career sacks.