The council created the medal in April 2023.
Ms Thompson told Tuesday’s full council meeting that when Zephaniah died, she made a promise to his family the city “would honour him in a significant way”.
“It’s fitting he is the first recipient of this medal because he spent his whole life breaking new ground.”
The authority agreed it should consult with Zephaniah’s family to make arrangements for awarding the medal within 12 months.
Giving a statement on behalf of family this month, his brother Tippa Naphtali said following Zephaniah’s death, his family were approached by “many individuals, organisations and institutions who wanted to stage events or initiatives in his memory”.
The family worked with more than 45 such parties nationally in the year following his passing, he added.
“Such was the strength of feeling in Birmingham, we have worked (and are still working) with third parties on a number of legacy projects.”
Mr Naphtali said up to his death Zephaniah remained committed to doing everything he could to promote the city “on a national and international stage”.
The poet was “passionate about giving the city the recognition and national profile” it deserved, he added.
