The Transocean Winner drilling rig was successfully refloated at high tide in Dalmore Bay, near Carloway, at around 10pm on Monday.
Two tug boats are taking the 17,000-tonne structure to Broad Bay, on the east side of the island, where experts will assess the damage.
Hugh Shaw, the official overseeing the operation, said he was pleased the refloating operation was completed successfully.
He said the journey to Broad Bay is taking longer than initially estimated, and the rig is now due to arrive at its destination in the early hours of Wednesday.
Mr Shaw, the Secretary of State’s representative for maritime salvage and intervention, told BBC Radio Scotland: “I think all the teams on board both the tugs and on the rig did a fantastic job and the rig is now on its way, albeit making a slow passage, but she’s heading round towards Broad Bay.”
He told the Good Morning Scotland programme: “We’d anticipated if we got her safely off we were looking at perhaps two to two-and-a-half knots to get her round the 54-mile passage.
“I spoke to the salvage master this morning. They’re making steady but slower progress than we had anticipated so she’s actually doing about 1.7 knots.
“So I’m not expecting her to arrive in Broad Bay now until perhaps the early hours of tomorrow morning.”
Eight anchors are being laid out in Broad Bay to hold the rig in place when it arrives.
Transocean will then begin the assessment process - which includes putting divers in the water - to look at the damage the rig has suffered; a process which could take until the middle of September.
Mr Shaw said: “There may be the opportunity to effect some temporary repairs in Broad Bay itself but that would only be very light engineering if we do anything there.”
Options after that include towing the rig to wherever Transocean intends to take it, or, if the damage is more significant, officials may consider bringing in a semi-submersible ship to move the vessel from Broad Bay.
Asked whether the rig could be decommissioned on Lewis, Mr Shaw said: “We are aware that there are facilities both up in the islands here and down the west coast of Scotland.
“We’ll simply look at what we have and try and piece some things together as the information comes in, but no decisions have been made regarding anything along the line at this stage.”
The semi-submersible structure was blown ashore at Dalmore during a towing operation on Monday August 8. The towline between the rig and its tug was lost en route from Norway to Malta amid high winds and heavy seas in the early hours that day.
The rig grounded with 280 tonnes of diesel on board and two of its four fuel tanks were damaged in the incident.
It resulted in the loss of 53,000 litres of fuel, most of which is thought to have evaporated with no damage to the environment.
The remaining 200 tonnes of hydrocarbons, mainly diesel oil with small amounts of base oil and brine, were transferred from the rig to the supply vessel Olympic Orion at the weekend.
Mr Shaw said the temporary exclusion zone remains in place at Dalmore while underwater surveys are carried out to ensure no debris has been left behind.
“Our aim is to try and get everything in the Dalmore area back to normality as soon as possible,” he added.
The Marine Accident Investigation Branch is carrying out a probe into the grounding of the rig and will issue its findings at a later date.