After a long search on the Internet. I discovered that Qt Installer Framework has necessary code to patch relocated Qt binaries under Mac OSX. There was small problem to run that code, it's written in C++ that was not that easy to compile since it depends on Qt4 while I'm using Qt5.1. Fortunately, it turned out that all the operations are available via command line. To use that commands you need any installer created with Qt Installer Framework (Qt binary installer for Mac OSX is good enough) and to use the command below:
./qt-mac-opensource-5.1.0-clang-offline.app/Contents/MacOS/qt-mac-opensource-5.1.0-clang-offline --runoperation "QtPatch" "mac"
"/Path/to/Qt/binaries/which/need/to/be/patched" "qt5"
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Operation was successfully performed.
In case you get an error message which says "qmake is not a program" or something like that try to chmod qmake:
chmod 777 qmake
Note: this works with any QtIFW installer. Play around with prebuilt version of QtIFW
OK, that's it, that's the most straight forward way I found so far.