Benteke, who signed a contract until 2024 with a one-year option, is reportedly becoming DC United's highest-paid player in the club's history, more than the $3.5million a season manager Wayne Rooney earned as player at the club.
The Belgian striker was a £32.5million club-record transfer under then Palace manager Alan Pardew in 2016, and made 177 appearace and scored 37 goals during his six-year stint at the club.
But chances to play in the Premier League have been limited and the 31-year-old made the decision to move before the 2-0 defeat to Arsenal on Friday night.
"This is something the player wanted to do," explained Vieira of Benteke's exit.
"When players want to play, and you can't guarantee them time or games, you have to let them go.
"Christian spent six years at this football club, and he was fantastic for the football club.
"This is something he wanted to do, and we wish him all the best."
Earlier this week the Palace boss admitted he was "short of numbers" and saw gaps all over the pitch.
"We're always looking to improve the team," Vieira added. "If we find the right players with the right budget we will try to do it.
"If not there are players here who will grow during the season, players who are prepared to work hard for the club, and we have to keep challenging those players."