Elliot has resigned from his roles as a member of the FA's judicial panel and as a nominated member of UEFA committees as well as his role as a Kick It Out trustee.
Following a failed business venture involving the two The Sun reported that Elliott, 48, texted Rufus the words: "Ur (sic) a stupid man n*****", adding: "You dog. Ur history my friend."
Elliott, made a CBE for his services to equality and diversity in football earlier this month, also allegedly texted Rufus: 'This will follow you scumbag.'
A statement released by the FA on Saturday read: "The FA has today accepted the resignation of Paul Elliott from all roles representing the organisation.
"This follows a conversation in which discriminatory abusive comments were made to Richard Rufus."