According to his new club, the 28-year-old was acquired in exchange for $100,000 in Targeted Allocation Money, $400,000 in General Allocation Money and an International Roster Spot.
Accam scored four goals and had two assists in eight appearances for Union this season.
"We want to welcome David Accam to Columbus Crew SC as David is a fast, dynamic player and a proven attacking threat in MLS,” Crew president Tim Bezbatchenko said in a club statement.
“In addition to having experience in the league, we believe David’s specific skillset will help us bolster the attack of our current roster and we look forward to his contributions to the club this season.”
Accam will join compatriots Harrison Afful, Jonathan Mensah and Edward Opoku, who already play for Crew.
He has earned nine caps with the Black Stars since making his debut in the 2015.
The Black Stars will open their campaign against Benin on June 25, face Cameroon on July 2 and wrap up the first round against Guinea-Bissau, who will be making only their second appearance at the continental showpiece.