Sheikh Abid Gulzar said he agreed the deal with owner Cuerden Leisure on Wednesday.
He would not disclose the cost, but the BBC understands it is less than the Â£5.5m asking price when the pier was last for sale in 2009.
Cuerden said the sale was not completed and it would comment later.
About one third of the 1870 Grade II* listed structure was destroyed in the blaze on 30 July 2014.
It was partially reopened in September 2014 but a large section remains empty.
The pier was put up for sale this summer when Eastbourne Borough Council refused Cuerden Leisure permission to install temporary children's rides on the vacant section of the structure.
Sheikh Gulzar, who owns two hotels in Eastbourne and another near Hailsham, said he was now "the daddy of the pier" but would work with the council to ensure any plans had its full approval.
"I have got a lot of love and affection for it and I will look after it," he said.
"I can see the pier from my bedroom."
Cuerden director St John Stott said: "A sale of Eastbourne Pier did not complete yesterday.
"We will let you have a statement if and when anything happens."
Chamber of Commerce chief executive Christina Ewbank said she was delighted a local business person was investing in the pier.
"If Abid Gulzar is looking at a series of changing events that will bring people on to the pier that can only be good," she said.
Council leader David Tutt said the council was keen to work with whoever owned the pier to ensure it remained the landmark attraction for Eastbourne.
The sale of Eastbourne Pier, badly damaged by fire 15 months ago, has been agreed according to a local hotel chain owner.