The Legend of Zelda: Breath Of The Wild” takes place after all of the other installments to the franchise, according to the official Nintendo Japan website and reported via SiliconEra.

During the weekend, Nintendo updated its Japanese Zelda webpage, which includes a timeline of the series, and placed the Nintendo Switch title “Breath of the Wild” at the very end. 2011’s “Skyward Sword” is, in contrast, placed at the very beginning of the timeline.
What complicates matters is that in “Ocarina of Time,” there are multiple outcomes for the player. The story ends with victory or with Link’s fall. Further, there is no indication whether or not “Breath of the Wild” occurs after the fallen hero or victory outcome in “Ocarina of Time.”
SiliconEra also notes that another change in the fallen hero timeline is that “Link’s Awakening” has now been moved to before the “Oracle of Ages” and  “Oracle of Seasons” games, and is now after “A Link to the Past.” This means that the fan theory that Link dies in “A Link to the Past” can be marked off completely, according to official canon.
Famitsu interviewed Eiji Aonuma, series producer, and Hidemaro Fujibayashi, “Breath of the Wild” game director regarding the changes to the timeline.
Aonuma acknowledged the confusion over the timeline and which “end” “Breath of the Wild” belongs to, while Fujibayashi stated that it is “up to the player’s imagination,” according to SiliconEra’s translation.
“Hyrule’s history changes with time,” Aonuma said. “When we think of the next game and what we want to do with it, we might think, ‘Oh, this’ll fit well,’ and place it neatly into the timeline, but sometimes we think, ‘Oh crap,’ and have to change the placement. Actually, the decided history has been tweaked many times.”
Fujibayashi then clarified that it’s not so much that Hyrule’s history changes as it is that “new information and truths come to light,” that apparently changes what the player knows and understands about the world.
To put that into plain speak: We still don’t know which timeline “Breath of the Wild” concludes, and Nintendo seems unlikely to know for sure (or at least confirm) either way.