Kovind and Teshome discussed economic relations, with the agreements on trade, communication and media signed in their presence, according to the president's Twitter page.
India also thanked Ethiopia for its participation in the International Solar Alliance (ISA), established in 2015.
The aim of the ISA is to provide a dedicated platform for cooperation among solar resource rich countries and promote the use of solar energy.
Later, Kovind and Teshome also addressed the India- Ethiopia Business Dialogue and released a book titled 'India- Ethiopia: 70 Years of Diplomatic Relations'.
The India Business Forum is the first partner-country forum of its kind in Ethiopia and represents more than 100 Indian companies.
Kovind said India has created jobs and contributed to the prosperity of Ethiopia.
Indian investment has had a significant presence in manufacturing in Ethiopia and value addition to local resources, he said.
Ethiopia has been the largest recipient of Indian concessional lines of credit in Africa, with over USD 1 billion committed.
Kovind arrived here from Djibouti yesterday on the second leg of his maiden visit abroad.
His visit is the first by an Indian president to Ethiopia in 45 years since President V V Giri's trip in 1972.
Last night, the president addressed the Indian community at an event in Addis Ababa, noting that it has been at the centre of India-Ethiopia relations.
As teachers and educators, Indians have given a helping hand to nation building in their host country. As entrepreneurs, they have created economic opportunities and imparted skills to local people, he said.
Kovind praised Indian technology professionals and workers for adding value to Ethiopian industry, saying that with hard work and dedication, the Indian community has built respect for itself within Ethiopian society.
Yet it has retained and carried forward Indian values, family traditions and work ethic while adapting very well to its adopted home, he said.
The event was attended by some 500 members of Ethiopia's Indian community which is spread all over the country and is 5,000-strong.