Yes, they're part of the Judicial branch, established by Article III of the US Constitution [1]. Not all judges are Article III judges with the protections mentioned therein, but all judges are part of the government on some level. You can see some measures to establish independence from the other branches as well as accountability if you read the section. For the subset of judges that are Article III judges, their wages cannot be reduced and they have a lifetime appointment "in good behavior" (which means they can be impeached for misconduct). What you won't find in the text is anything about judicial review of laws. The court came up with that doctrine on its own in Marbury v. Madison. [2]

[1] http://www.archives.gov/exhibits/charters/constitution_trans...

[2] https://en.wikipedia.org/wiki/Marbury_v._Madison