The Giants (3-11) officially cleared Jones to return on Friday. He practiced without limitations this week.
Coach Pat Shurmur said Jones will start, barring anything unforeseen, while veteran Eli Manning heads back to the bench.
"He looked good," Shurmur said of Jones this week. "He's prepared and ready to go."
Manning started the past two weeks and helped the Giants snap a nine-game losing streak. They defeated the Miami Dolphins at home in a game that was treated by fans as a sendoff for Manning.
The Giants were always going back to Jones as the starter when he was healthy. He is their future as the No. 6 overall pick in this year's draft.
Manning, 38, is set to become a free agent at the end of the season. The two-time Super Bowl winner has thrown six touchdown passes with five interceptions in his 16th season with the Giants.
Jones hurt his ankle early this month in a loss to the Green Bay Packers. He ditched the walking boot on his right foot last Monday and was a limited participant in practice last week. He was a full participant this week.
"It feels good. It feels like I can do everything I need to do," Jones said earlier this week. "Keep working through and hopefully I can continue to improve throughout the week."
Jones took almost all of the first-team snaps at practice. His return sets up a matchup between first-round quarterbacks with Dwayne Haskins starting for Washington. Haskins was the 15th overall pick in the draft.
Jones has thrown 18 touchdown passes with 11 interceptions in 10 starts during his rookie season. He also has a league-high 10 lost fumbles. That will be a focus Sunday as he tries to play his first clean game as a professional while snapping an eight-game skid as a starter.
"Ball security is obviously the big thing [to polish up], and making sure that I'm doing my part in protecting the ball. Making sure as an offense we're protecting the ball," Jones said. "That way it gives us the best chance to win. That's the most important thing in these last two weeks, is to win games."