It said the movie was illegally downloaded 47 million times between 1 January and 25 December.
That beats the figure for last year's list-topper, the Wolf of Wall Street, which was downloaded 30 million times.
All of this year's top 10 most pirated films had over 30 million downloads, Excipio said.
"If you compare last year's top 10 to this year the increase is enormous," spokesman Benjamin Hauck told the BBC.
According to the firm, the top 10 most pirated movies of 2015 were:
Separate research from the news site TorrentFreak indicated that Game of Thrones was the most pirated television show for the fourth year in a row.
The fantasy-based drama, produced by HBO, was downloaded an estimated 14.4 million times via BitTorrent - up from eight million times last year
That does not include illegal online streaming or file-hosting services, TorrentFreak said, meaning total piracy numbers would be higher.
"The number of downloads for the top TV shows appears to be increasing," added TorrentFreak's editor Ernesto van der Sar.
"For some shows it is even exceeding the number of traditional viewers in the US."
The news may surprise some, given the rise of subscription video on demand services such as Netflix and Amazon Prime.
However, Mark Mulligan of Midia Research said these services were still in their "infancy, and only have a slice of the content available".
"To watch all of those popular TV shows legally, without a cable TV subscription, you'd need to pay $45 (Â£30) a month in the US across five different streaming services.
"And if you don't happen to live in the US, hard luck, many of those shows are only available online with a pay-TV subscription."
Mr van der Sar said the rise in internet connectivity in developing nations might also be pushing up the numbers.
According to Excipio, Brazil was responsible for the most illegal film downloads this year, followed by Russia, China and India.
The US was positioned fifth, down from third last year, and the UK seventh, down from sixth.
According to TorrentFreak, the top 10 pirated television shows of 2015 were:
Interstellar has topped the list of the most pirated films of 2015, according to piracy tracking firm Excipio.