The vessel was refloated and guided back to port in May after spending two months stuck in the wreckage with a massive steel truss draped across its damaged bow.
A National Transportation Safety Board (NTSB) investigation found the ship experienced two power outages in the hours before it left the Port of Baltimore.
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Timeline of Baltimore bridge collapse
It lost power again and veered off course before crashing into the bridge.
The ship’s crew, who had been forced to stay in the country afterwards, have been allowed to leave, provided they were available to give evidence, thanks to an agreement confirmed by a federal judge.
Earlier on Monday, four tugboats helped the 984ft (300m) craft get moving shortly before 8.30am.
The Dali is scheduled to go directly to Virginia International Gateway where around 1,500 cargo containers will be offloaded to reduce draft, the US Coast Guard said in a statement.
From there, the vessel is scheduled to sail for Virginia’s Norfolk International Terminal for further salvage and repairs from damage caused during the bridge collapse.
The Dali was sailing under its own power with a full crew of 22 and six salvage experts, according to the coast guard, which is overseeing the voyage and providing a 500-yard (457m) safety zone around it.