The 20-year-old has signed a contract running until the summer of 2030 in a deal worth around €6m, a club-record fee for Elversberg, with Borussia Dortmund retaining a buy-back option.
Campbell made seven competitive appearances for Dortmund's first team, including in the Champions League, before spending the second half of last season on loan at Hoffenheim, where he added five Bundesliga appearances.
Sporting director Christian Weber said the club had been tracking Campbell for some time.
"With Cole we have signed another highly talented player who will be a huge asset to us with his exceptional pace and individual skills," Weber told the club website. "We have been chasing him for a good while and are delighted that he has chosen us."
Campbell said he was looking forward to the new challenge.
"The discussions with those in charge were very open from the start and have continued to develop positively," he said.
"I feel like I'm joining an exciting team with a lot of potential, where I can make a valuable contribution. That's why I'm certain this move to Elversberg is exactly the right one. I'm looking forward to the team and this new chapter at the club."
Born in Houston and holding both American and Icelandic citizenship, Campbell began his career at FH Hafnarfjordur in Iceland after his family relocated there, making his senior debut at 15, before a short spell at Breidablik preceded his move to Dortmund's academy in the summer of 2022.
Campbell progressed steadily through Dortmund's youth ranks before earning a place in the first-team picture, though regular football proved hard to come by at one of Europe's biggest clubs. His loan spell at TSG Hoffenheim in the second half of last season was designed to give him more consistent senior minutes, and the move to Elversberg now offers a fresh platform in the Bundesliga proper following the Saarland club's promotion.
Elversberg's rise to the top flight is a significant achievement, and head coach Vincent Wagner is expected to lean on a mix of experience and promising young talent like Campbell as they prepare for life among Germany's elite.
The American, who has represented the United States at youth level, will hope to use the platform to force his way into wider international recognition as he continues his development away from Dortmund.