Hartson, capped 51 times, was prepared to leave in the wake of media criticism of Coleman's backroom team.
"I've offered to resign a couple of times in the last couple of months but Chris wants me there," he said.
"He feels I've got a lot to offer the players having played up front on my own for 10 years for Wales.
"You're always going to get criticism. I'm very relaxed about it. I've come through cancer for goodness sake - I don't worry about coaching roles with Wales."
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