The shortstop, selected 13th overall by San Diego in the June 2014 draft, was part of a three-team trade in December that sent 2013 AL Rookie of the Year Wil Myers to the Padres.
Turner had to wait to join his new team, however, due to Major League Rule 3(b)(6), which states that a draft pick cannot be traded until one year after he signs his initial contract. Also, Rule 12(e)(2) says teams have six months from the time of a trade to finalize a player to be named.
Major League Baseball and the players' association agreed to change the rule in May but that tweak only applies to future drafts.
Turner hit .322 at Double-A for the Padres organization. The Nationals plan to assign Turner to Double-A Harrisburg.
"From the outset, this was a complex deal, but we thought it was one that would better our organization for the present as well as the long term," Nationals general manager Mike Rizzo said.
Ross threw eight solid innings to pick up his first career win in the majors on Saturday when Washington beat the Milwaukee Brewers 7-2.
The Associated Press contributed to this report.