The Modern Express was carrying diggers and 3,600 tonnes of timber from Gabon in west Africa to the port of Le Havre in Normandy, France when it ran into difficulties in late January.
The ship, registered in Panama, has been under tow by the Spanish tugboat the Centaurus since Monday.
By late Tuesday it was some 10 nautical miles (18.5 kilometres) from Bilbao, according to Spanish authorities, who decided to delay the operation to bring it into port until daylight Wednesday.
"We began manoeuvres around 9:30 am (0830 GMT)," a port spokesman told AFP, adding that they would take at least a few hours.
The ship's crew sent a distress signal on January 27th after the vessel listed strongly to one side, probably due to its cargo coming loose in the hull.
After seven days drifting in rough seas, it was only 44 kilometres (27 miles) from the French coast when authorities launched a final bid to attach a tow line and stop it from hitting the shore.
Experts from Dutch company SMIT Salvage, which specialises in helping ships in distress, were lowered by helicopter onto the vessel as it tilted at 40 to 50 degrees while buffeted by large waves.
The 22 crew were evacuated by helicopter as they clung to the ship.
See video of the rescue:
The Bilbao operation is the biggest ever organised by the port, one of the biggest on Spain's Atlantic coast which handled some 31 million tonnes of freight in 2014.