The 37-year-old won 51 caps for his country and also played for several clubs including Arsenal, West Ham and Celtic.
"Chris simply asked me: 'Would you like to come and work for me?' I immediately accepted, shook his hand and promised him I'd do anything possible to help make the Wales national team successful," Hartson said in the Scottish Sun.
Coleman became Wales manager in January 2012, following the death of predecessor Gary Speed in November 2011.
Hartson also expressed an interest in becoming Wales boss before Coleman was appointed.
Swansea-bred Hartson added: "Everyone knows how much of a patriot I am. I speak our native language.
"So as a proud Swansea boy - just like Chris incidentally - to now be involved with the team is immensely satisfying.
"To be assisting Chris to effectively answer a call from my country is a fantastic privilege and honour for me.
"It's also why I'll be giving up my media duties to ensure I perform to the best of my ability."
The Football Association of Wales is yet to comment.