Johnson will manage the rest of the season and his first game will be Monday against hte Lost Angeles Angels. He has been a senior advisor with the team since 2009, though he hasn't managed in the big leagues since 2000 with the Los Angeles Dodgers.
Johnson also agreed to a three-years consulting contract that will allow him to remain with the team and participate in the selection of a successor.
Interim manager John McLaren ran the team for the third straight game in Sunday's series finale against the Chicago White Sox. Riggleman's former bench coach will leave the team after the game and be reassigned to scouting duties with the organization.
The 68-year-old Johnson managed the Mets, Dodgers, Reds and Orioles over 14 seasons and compiled a 1148-888 record. He led the 1986 Mets to a World Series championship and 11 of his teams finished first or second 14 times.
Even though he hasn't managed in the majors for 11 years, Johnson did skipper Team USA in the 2009 World Baseball Classic, the 2008 Olympic team in Beijing, and two summers ago managed amateur players in a Florida summer collegiate league.
Riggleman resigned abruptly Thursday after the Nationals beat Seattle, unhappy that general manager Mike Rizzo declined to have a conversation about picking up his option for 2012. The departure was stunning for its timing -- the Nationals have won 12 of their last 14 games.
It was the second time in a week a manager has resigned and been replaced. Florida skipper Edwin Rodriguez quit last Sunday and was replaced by 80-year-old Jack McKeon.
"I know they've got great vision here. I know Davey Johnson is gonna do a great job here," McLaren said before his final game Sunday. McLaren said he met with Nationals players in groups to tell them about his future.
"I didn't want them to not hear it from me," McLaren said. "I feel bad about Jim Riggleman. It's a tough situation for everybody. He's a good friend. I wish it hadn't gone down like this, but it did and I think we'll move on."