Like every other Backwards Compatible game, players will be able to carry over previous game saves via cloud storage, achievements and DLC. 

With this announcement, every Borderlands title to date will now be available to Xbox One users. Borderlands 2 and Borderlands: The Pre-Sequel recently got the HD re-release treatment in Borderlands: The Handsome Collection, which released back in March to the chagrin of some of the early adopters of The Pre-Sequel. It was a bit odd that the Handsome Collection omitted the first game in the series, but with this announcement, it is now a non-issue.