The Ocean Nova cruise ship docked at Lisahally on Tuesday.
Mr Eastwood was speaking after it was revealed this week that 12,000 cruise passengers are due to arrive in Derry by the 2015.
The first cruise ship of the year arrived in the city on Tuesday. The Ocean Nova is a specialist vessel carrying a group of bird watching (ornithology) enthusiasts.
Derry was added as a late addition to their itinerary because of the richness of local wildlife.
A total of 11 cruise ships are expected to dock along the Foyle in 2015, with a further 10 already booked for 2016.
Mr Eastwood commended the hard work carried out by local agencies in successfully promoting the region to cruise lines.
He said: “The first of a fleet of cruise ships due to dock in Derry this year has arrived at Lisahally to get the Foyle cruise season off and running.
“With some 12,000 passengers expected to disembark at Greencastle, Lisahally and Meadowbank during 2015 the industry has shown tremendous growth down to the hard work of agencies such as Visit Derry, Foyle Port, the local council and the Loughs Agency.
“The industry has shown tremendous growth down to the hard work of agencies such as Visit Derry, Foyle Port, the local council and the Loughs Agency.
“The success in targeting cruise lines to choose our city shows the great potential that exists to grow the industry.
“Derry is the obvious stopover for cruise visitors to take best advantage of the great tourism offering in the North West of Ireland.
“A lot of work has gone into telling the world what we have to offer and with a continued focus I believe we can make Derry a favourite European cruise destination.”
Odhran Dunne, general manager with Visit Derry, revealed to the Journal this week that the cruise visitors are expected to provide an economic boost to the tune of £800,000 this year.
Mr Dunne said: “We have been working hard within the cruise market to increase the number of visiting cruise ships and we are really happy with the numbers coming through in 2015.
“We are working with Foyle Port, the Council and Loughs Agency to target cruise ships and it has worked really well for us.”
Once they arrive, he added, passengers are greeted and have the option of taking on several local tours and trips across Derry, Inishowen, Glenveagh National Park and Castle, Giants Causeway, the Sperrins.
Mr Dunne said the next ship was due in June, while the largest vessel arriving locally will be the Crystal Serenity on August 3.