After doing some research, partially on the Stack Overflow, I decided to try Boost.Log library by Andrey Semashev.
Unfortunately, to build the Boost.Log library I have to place it in the Boost source tree and compile as it was part of the Boost. It is a blocker for me, because I have already somewhat complicated building configuration. I want to build Boost.Log standalone.
I've found interesting thread on Boost.Log forum, but this method doesn't work for me.