Azeb, born in Wolqayt, was married to Ethiopian Prime Minister Meles Zenawi until his death in 2012. Together they had three children: Semhal, Marda and Senay Meles. She was elected in 2005 to the House of Peoples' Representatives (the lower House of the Ethiopian Parliament) representing her home woreda of Wolqayt and Humera, and serves as chair of its Social Affairs Standing Committee. Her role has at times been controversial, with some members of Ethiopia's diaspora alleging that, during the period in which she was an executive at the parastatal Mega Corporation, she was involved in "the impropriety of mingling public, private and party-owned businesses."
However Azeb is also known for her work to teach rural Ethiopians about the issues of HIV/AIDS Her appearance at a special ceremony to honor the First Ladies of Africa for their efforts against the spread of HIV/AIDS held by Georgetown University of Washington DC on 15 January 2007 was met by protests of exiled Ethiopians."The University was awarding its "John Thompson Legacy of a Dream Award" to the Organisation of African First Ladies against HIV/AIDS for its leadership and service toward the ideals of Dr. Martin Luther King, Jr. Mesfin was to accept the award on behalf of the organization along with the first ladies of Zambia and Rwanda. She started the organization "Ethiopian Coalition of Women against HIV/AIDS" and continues to work closely with community leaders to ensure the rights of women,fight harmful traditional practices and HIV/AIDS.She said the award she received is not just for her organization but for the entire Ethiopian women declaring "the award is the result of the relentless struggle waged by Ethiopian women."