Snyder has said that it is a different Batman than the one from the Nolan movies.
From an interview with The Daily Beast
Only in that because it’s a different Batman than the Batman that was in the Chris Nolan movies, so we have a little bit more explaining to do—and you just had a whole Superman movie. But I think only in that way, because you need to understand where Batman is with everything. And that’s more toward the beginning, but it evens back out as it goes on.
Snyder also said that he tried to emulate the universe Nolan created.
“It’s a tricky process, setting up the DC universe, or Justice League,” Snyder said. “The credit goes to [Batman Begins director] Chris Nolan because he set the die for the DC Universe in a great way that I tried to emulate. I look at it as more being mythological than, say, bubblegum. And I think that that’s appropriate for Batman and Superman because they’re the most mythological of our superheroes.”
Less canonically, Christian Bale told IGN that the Nolan Batman doesn't belong in any other movies. (This quote can be interpreted as purely his opinion)
The actor reflected that, though he thinks that The Dark Knight is a "character that could have kept on going and going and going," that ultimately, "it was right for Chris [Nolan] to finish it where he did."
Adding, "And ours doesn't belong in any other version at all."