The band scrapped their appearance in Fort Lauderdale, Florida, on Wednesday due to power outages and curfews resulting from last week's storm. They will now launch their Playing The Angel tour in St Petersburg, western Florida, on Thursday night.
The electro-pop band, best known for hits like Just Can't Get Enough, last toured the US in 2001, BBC News reports.
Hurricane Wilma struck Florida's southwest coast on 24 October, and crossed the peninsula to the Miami, Fort Lauderdale, West Palm Beach region, leaving millions without power.
Most of it has been restored, but the area is still affected by debris, downed power lines and trees.
The situation led Depeche Mode to cancel the concert at Fort Lauderdale's Bank Atlantic Center.
The tour, which comes in support of the group's new album, "Playing the Angel," will now begin Thursday in St. Petersburg, Fla, reuters reports. A.M.