Pat Chun, FAU director of athletics, said the pair had stepped down not because of the Owls' 2-6 start to the season, but for drug use.
"It is with profound disappointment and sadness that I announce the resignation of (Pelini and Rekstis)," Chun said in a statement. "They tendered their resignations to me late this morning after I confronted both coaches with reports relating to their use of illegal drugs."
Chun said he was "made aware of these concerns" Monday and immediately reported the allegations to the school's lawyer, followed by "quick and decisive action."
"I can assure you that we have no information that suggests anyone other than these two individuals engaged in these activities," he said, adding, "I am personally very saddened for our student-athletes, coaches and staff."
The team reacted with "shock, dismay and disbelief" at the news, the AD said.
Owls offensive coordinator Brian Wright has taken over as interim head coach.
"I apologize for exercising poor judgment," Pelini said in a statement. "My greatest concerns at this time are for my family, the dedicated FAU players and my staff."