A large French fishing ship began towing the liner to port on Tuesday.
A Seychelles Coast Guard ship reached the Costa Allegra later in the day, along with two tugboats from the Seychelles Ports Authority, said Seychelles presidential spokeswoman Srdjana Janosevic.
The ship was towed to Port Victoria, the Seychelles capital.
The impact the incident could have on Costa's business is hard to predict. After the Concordia disaster, the company had a 35% drop in bookings, Stiekema said.