The team was established in 1932 as the Boston Braves and took on its current name in 1933 before moving to Washington DC four years later.
Until now, team owner Snyder had emphatically rejected requests to drop the Redskins tag.
"We'll never change the name," he told in 2013. "It's that simple. NEVER - you can use caps."
President Donald Trump meanwhile had criticised Washington's announcement that the team name was under review.
"They name teams out of STRENGTH, not weakness, but now the Washington Redskins & Cleveland Indians, two fabled sports franchises, look like they are going to be changing their names in order to be politically correct," Trump tweeted last week.
Washington's statement on Monday said Snyder and head coach Ron Rivera were "working closely to develop a new name and design approach that will enhance the standing of our proud, tradition rich franchise and inspire our sponsors, fans and community for the next 100 years".
The reported that the team had a preferred choice for a replacement name, but were working through trademark issues surrounding the tag.
Rivera, one of only a handful of minority head coaches in the NFL, said earlier this month that he believed the new name be respectful of Native American culture and the military.