Instead of installing SSDT on the server, installing latest SSMS (v17.2 in my case) along with v16.5.3 solved the issue. Both ssms versions were installed side by side.

http://msdn.microsoft.com/en-us/library/dd638062(v=sql.100).aspx

if you find the above steps confusing use this tool :

http://sqlslipstreamer.codeplex.com/

Thanks Guys,

I had the same issue. My pasword for the SQL full text service expired. I updated the password of this service and back up job is happy now.  This issue...